## 2020

**4/2, Aleksej Zelezniak, Chalmers: Uncovering genotype-phenotype relationships using artificial intelligence**

Abstract:

Understanding the genetic regulatory code that governs gene expression is a primary, yet challenging aspiration in molecular biology that opens up possibilities to cure human diseases and solve biotechnology problems. I will present two our recent works (1,2). First, I will demonstrate how we applied deep learning on over 20,000 mRNA datasets to learn the genetic regulatory code controlling mRNA expression in 7 model organisms ranging from bacteria to human. There, we show that in all organisms, mRNA abundance can be predicted directly from the DNA sequence with high accuracy, demonstrating that up to 82% of the variation of gene expression levels is encoded in the gene regulatory structure. In second study, I will present a ProteinGAN, a specialised variant of the generative adversarial network that is able to ‘learn’ natural protein sequence diversity and enables the generation of functional protein sequences. We tested ProteinGAN experimentally showing that learns the evolutionary relationships of protein sequences directly from the complex multidimensional amino acid sequence space and creates new, highly diverse functional sequence variants with natural-like physical properties. ProteinGAN therefore demonstrates the potential of artificial intelligence to rapidly generate highly diverse novel functional proteins within the allowed biological constraints of the sequence space.

1) Zrimec J et al “Gene expression is encoded in all parts of a co-evolving interacting gene regulatory structure”, biorxiv, https://doi.org/10.1101/792531

2) Repecka D et al, "Expanding functional protein sequence space using generative adversarial networks”, biorxiv, https://doi.org/10.1101/789719

Understanding the genetic regulatory code that governs gene expression is a primary, yet challenging aspiration in molecular biology that opens up possibilities to cure human diseases and solve biotechnology problems. I will present two our recent works (1,2). First, I will demonstrate how we applied deep learning on over 20,000 mRNA datasets to learn the genetic regulatory code controlling mRNA expression in 7 model organisms ranging from bacteria to human. There, we show that in all organisms, mRNA abundance can be predicted directly from the DNA sequence with high accuracy, demonstrating that up to 82% of the variation of gene expression levels is encoded in the gene regulatory structure. In second study, I will present a ProteinGAN, a specialised variant of the generative adversarial network that is able to ‘learn’ natural protein sequence diversity and enables the generation of functional protein sequences. We tested ProteinGAN experimentally showing that learns the evolutionary relationships of protein sequences directly from the complex multidimensional amino acid sequence space and creates new, highly diverse functional sequence variants with natural-like physical properties. ProteinGAN therefore demonstrates the potential of artificial intelligence to rapidly generate highly diverse novel functional proteins within the allowed biological constraints of the sequence space.

1) Zrimec J et al “Gene expression is encoded in all parts of a co-evolving interacting gene regulatory structure”, biorxiv, https://doi.org/10.1101/792531

2) Repecka D et al, "Expanding functional protein sequence space using generative adversarial networks”, biorxiv, https://doi.org/10.1101/789719

**11/2, Henrik Imberg, Chalmers: Optimal sampling in unbiased active learning**

Abstract: We study the statistical properties of weighted estimators in unbiased pool-based active learning where instances are sampled at random with unequal probabilities. For classification problems, the use of probabilistic uncertainty sampling has previously been suggested for such algorithms, motivated by the heuristic argument that this would target the most informative instances, and further by the assertion that this also would minimise the variance of the estimated (logarithmic) loss. We argue that probabilistic uncertainty sampling does, in fact, not reach any of these targets.

Considering a general family of parametric prediction models, we derive asymptotic expansions for the mean squared prediction error and for the variance of the total loss, and consequently present sampling schemes that minimise these quantities. We show that the resulting sampling schemes depend both on label uncertainty and on the influence on model fitting through the location of data points in the feature space, and have a close connection to statistical leverage.

The proposed active learning algorithm is evaluated on a number of datasets, and we demonstrate better predictive performance than competing methods on all benchmark datasets. In contrast, deterministic uncertainty sampling always performed worse than simple random sampling, as did probabilistic uncertainty sampling in one of the examples.

Considering a general family of parametric prediction models, we derive asymptotic expansions for the mean squared prediction error and for the variance of the total loss, and consequently present sampling schemes that minimise these quantities. We show that the resulting sampling schemes depend both on label uncertainty and on the influence on model fitting through the location of data points in the feature space, and have a close connection to statistical leverage.

The proposed active learning algorithm is evaluated on a number of datasets, and we demonstrate better predictive performance than competing methods on all benchmark datasets. In contrast, deterministic uncertainty sampling always performed worse than simple random sampling, as did probabilistic uncertainty sampling in one of the examples.

**18/2, Ottmar Cronie, Department of Public Health and Community Medicine, University of Gothenburg, and Department of Mathematics and Mathematical Statistics, Umeå University: Resample-smoothing and its application to Voronoi estimators**Adaptive non-parametric estimators of point process intensity functions tend to have the drawback that they under-smooth in regions where the density of the observed point pattern is high, and over-smooth where the point density is low. Voronoi estimators, which is one such example, are such that the intensity estimate at a given location is equal to the reciprocal of the size of the Voronoi/Dirichlet cell containing that location. To remedy the over-/under-smoothing issue, we introduce an additional smoothing operation, based on resampling the point pattern/process by independent random thinning, which we refer to as ”resample-smoothing”, and apply it to the Voronoi estimator. In addition, we study statistical properties such as unbiasedness and variance, and propose a rule-of-thumb and a data-driven cross-validation approach to choose the amount of smoothing to apply. Through a simulation study we show that our resample-smoothing technique improves the estimation substantially and that it generally performs better than single-bandwidth kernel estimation (in combination with the state of the art in bandwidth selection). We finally apply our proposed intensity estimation scheme to real data.

**10/3, Nikolaos Kourentzes, University of Skövde: Predicting with hierarchies**Abstract: Predictive problems often exhibit some hierarchical structure. For instance, in supply chains, demand over different products aggregates to the total demand per store, and demand across stores aggregates to the total demand over a region and so on. Several applications can be seen in a hierarchical context. Modelling the different levels of the hierarchy can provide us with additional information that can improve the quality of predictions across the whole hierarchy, enriching supported decisions and insights. In this talk we present the mechanics of hierarchical modelling and proceed to discuss recent innovations. We look in some detail the cases of cross-sectional and temporal hierarchies that are applicable to a wide range of time series problems and the newer possibilistic hierarchies that address classification and clustering problems. We provide the theoretical arguments favouring hierarchical approaches and use a number of empirical cases to demonstrate their flexibility and efficacy.

**17/3, Mike Pereira, Chalmers: A matrix-free approach to deal with non-stationary Gaussian random fields in geostatistical applications**Abstract: Geostatistics is the branch of Statistics attached to model spatial phenomena through probabilistic models. In particular, the spatial phenomenon is described by a (generally Gaussian) random field, and the observed data are considered as resulting from a particular realization of this random field. To facilitate the modeling and the subsequent geostatistical operations applied to the data, the random field is usually assumed to be stationary, thus meaning that the spatial structure of the data replicates across the domain of study.

However, when dealing with complex spatial datasets, this assumption becomes ill-adapted. Indeed, what about the case where the data clearly display a spatial structure that varies across the domain? Using more complex models (when it is possible) generally comes at the price of a drastic increase in operational costs (computational and storage-wise), rendering them hard to apply to large datasets.

In this work, we propose a solution to this problem, which relies on the definition of a class of random fields on Riemannian manifolds. These fields extend ongoing work that has been done to leverage a characterization of the random fields classically used in Geostatistics as solutions of stochastic partial differential equations. The discretization of these generalized random fields, undertaken using a finite element approach, then provides an explicit characterization that is leveraged to solve the scalability problem. Indeed, matrix-free algorithms, in the sense that they do not require to build and store any covariance (or precision) matrix, are derived to tackle for instance the simulation of large Gaussian vectors with given covariance properties, even in the non-stationary setting.

**24/3, Valeria Vitelli, Department of Biostatistics, University of Oslo: A novel Variational Bayes approach to Preference Learning with the Mallows rank model**Abstract: ranking data are ubiquitous in the digitalized society: we rank items as citizens, consumers, patients, and we receive recommendations based on estimates of our preferences. We have previously proposed a Bayesian preference learning framework based on the Mallows rank model, capable of jointly estimating the items consensus ranking, and of providing personalized accurate and diverse recommendations, also in the presence of heterogeneity and data inconsistencies. The Bayesian paradigm allows proper propagation of uncertainties, and provides probabilistic recommendations. The main bottleneck has shown to be computational: the current MCMC implementation, which manages up to thousands of users and hundreds of items, mixes slowly, and does not scale to meet the demands of realistic applications. Here we propose a Variational Bayes approach to performing posterior inference for the Mallows model, based on a pseudo-marginal approximating distribution that scans the items one by one: the novel inferential approach supports several data types, it has nice theoretical properties, and it shows a dramatic computational improvement in larger applications. We introduce this novel approach, together with empirical investigations of its performance, and a real case study on clicking data from the Norwegian Broadcasting Company (NRK).

**21/4, Rasmus Pedersen, Roskilde Universitet: Modelling Hematopoietic Stem Cells and their Interaction with the Bone Marrow Micro-Environment**Abstract:

Blood cell formation (hematopoiesis) is a process maintained by the hematopietic stem cells (HSCs) from within the bone marrow. HSCs give rise to progenitors which in turn produce the vast amount of cells located in the blood. HSCs are capable of self-renewal, and hence a sustained production of cells is possible, without exhaustion of the HSCs pool.

Mutations in the HSC genome give rise to a wide range of hematologic malignancies, such as acute myeloid leukemia (AML) or the myeloproliferative neoplasms (MPNs). As HSCs are difficult to investigate experimentally, mathematical modelling of HSC and blood dynamics is a useful tool in the battle against blood cancers.

We have developed a mechanism-based mathematical model of the HSCs and their interaction with the bone marrow micro-environment. Specifically, the model directly considers the reversible binding of HSCs to their specific niches, often omitted in other modelling works. In my talk, I will discuss some of the aspects of developing the model and the immediate results that arise from the model, which includes an expression of HSC fitness and insight about outcomes of bone marrow transplantation. To relate the HSC dynamics to observable measures such as blood-cell count, the model is reduced and incorporated into a separate model of the blood system. The combined model is compared with a vast data-set of blood measurements of MPN-diagnosed patients during treatment.By including the biological effects of the treatment used in the model, patient trajectories can be modelled to a satisfying degree. Such insights from the model show great promise for future predictions of patient responses and design of optimal treatment schemes.

Blood cell formation (hematopoiesis) is a process maintained by the hematopietic stem cells (HSCs) from within the bone marrow. HSCs give rise to progenitors which in turn produce the vast amount of cells located in the blood. HSCs are capable of self-renewal, and hence a sustained production of cells is possible, without exhaustion of the HSCs pool.

Mutations in the HSC genome give rise to a wide range of hematologic malignancies, such as acute myeloid leukemia (AML) or the myeloproliferative neoplasms (MPNs). As HSCs are difficult to investigate experimentally, mathematical modelling of HSC and blood dynamics is a useful tool in the battle against blood cancers.

We have developed a mechanism-based mathematical model of the HSCs and their interaction with the bone marrow micro-environment. Specifically, the model directly considers the reversible binding of HSCs to their specific niches, often omitted in other modelling works. In my talk, I will discuss some of the aspects of developing the model and the immediate results that arise from the model, which includes an expression of HSC fitness and insight about outcomes of bone marrow transplantation. To relate the HSC dynamics to observable measures such as blood-cell count, the model is reduced and incorporated into a separate model of the blood system. The combined model is compared with a vast data-set of blood measurements of MPN-diagnosed patients during treatment.By including the biological effects of the treatment used in the model, patient trajectories can be modelled to a satisfying degree. Such insights from the model show great promise for future predictions of patient responses and design of optimal treatment schemes.

**28/4, András Bálint, Chalmers: Mathematical methods in the analysis of traffic safety data**

Abstract: This talk describes real-world examples related to traffic safety research in which mathematical methods or models have been applied or should be applied. Relevant data sources and current research challenges as well as potential approaches will be discussed. One example is presented in greater detail, namely the analysis of multitasking additional-to-driving (MAD) under various conditions. Results from an analysis of the Second Strategic Highway Research Program Naturalistic Driving Study (SHRP2 NDS) show that the number of secondary tasks that the drivers were engaged in differs substantially for different event types. A graphical representation is presented that allows mapping task prevalence and co-occurrence within an event type as well as a comparison between different event types. Odds ratios computed in the study indicate an elevated risk for all safety-critical events associated with MAD compared to no task engagement, with the greatest increase in the risk of rear-end striking crashes. The results are similar irrespective of whether secondary tasks are defined as in SHRP2 or in terms of general task groups. The results confirm that the reduction of driving performance from MAD observed in simulator studies is manifested in real-world crashes as well.

**23/6, Chris Drovandi, Queensland University of Technology, Australia: Accelerating sequential Monte Carlo with surrogate likelihoods**

Abstract: Delayed-acceptance is a technique for reducing computational effort for Bayesian models with expensive likelihoods. Using delayed-acceptance kernels in MCMC can reduce the number of expensive likelihoods evaluations required to approximate a posterior expectation to a given accuracy. It uses a surrogate, or approximate, likelihood to avoid evaluation of the expensive likelihood when possible. Importantly, delayed-acceptance kernels preserve the intended targeted distribution of the Markov chain, when viewed as an extension of a Metropolis-Hastings kernel. Within the sequential Monte Carlo (SMC) framework, we utilise the history of the sampler to adaptively tune the surrogate likelihood to yield better approximations of the expensive likelihood, and use a surrogate first annealing schedule to further increase computational efficiency. Moreover, we propose a framework for optimising computation time whilst avoiding particles degeneracy, which encapsulates existing strategies in the literature. Overall, we develop a novel algorithm for computationally efficient SMC with expensive likelihood functions. The method is applied to static Bayesian models, which we demonstrate on toy and real examples.

[This work is led by PhD student Joshua Bon (Queensland University of Technology) and is in collaboration with Professor Anthony Lee (University of Bristol)]

[This work is led by PhD student Joshua Bon (Queensland University of Technology) and is in collaboration with Professor Anthony Lee (University of Bristol)]

**13/10, Raphaël Huser, KAUST: Estimating high-resolution Red Sea surface temperature hotspots, using a low-rank semiparametric spatial model**Abstract: In this work, we estimate extreme sea surface temperature (SST) hotspots, i.e., high threshold exceedance regions, for the Red Sea, a vital region of high biodiversity. We analyze high-resolution satellite-derived SST data comprising daily measurements at 16703 grid cells across the Red Sea over the period 1985–2015. We propose a semiparametric Bayesian spatial mixed-effects linear model with a flexible mean structure to capture spatially-varying trend and seasonality, while the residual spatial variability is modelled through a Dirichlet process mixture (DPM) of low-rank spatial Student-t processes (LTPs). By specifying cluster-specific parameters for each LTP mixture component, the bulk of the SST residuals influence tail inference and hotspot estimation only moderately. Our proposed model has a nonstationary mean, covariance and tail dependence, and posterior inference can be drawn efficiently through Gibbs sampling. In our application, we show that the proposed method outperforms some natural parametric and semiparametric alternatives. Moreover, we show how hotspots can be identified and we estimate extreme SST hotspots for the whole Red Sea, projected for the year 2100. The estimated 95% credible region for joint high threshold exceedances include large areas covering major endangered coral reefs in the southern Red Sea.

**20/10, Luigi Acerbi, University of Helsinki: Practical sample-efficient Bayesian inference for models with and without likelihoods**Abstract: Bayesian inference in applied fields of science and engineering can be challenging because in the best-case scenario the likelihood is a black-box (e.g., mildly-to-very expensive, no gradients) and more often than not it is not even available, with the researcher being only able to simulate data from the model. In this talk, I review a recent sample-efficient framework for approximate Bayesian inference, Variational Bayesian Monte Carlo (VBMC), which uses only a limited number of potentially noisy log-likelihood evaluations. VBMC produces both a nonparametric approximation of the posterior distribution and an approximate lower bound of the model evidence, useful for model selection. VBMC combines well with a technique we (re)introduced, inverse binomial sampling (IBS), that obtains unbiased and normally-distributed estimates of the log-likelihood via simulation. VBMC has been tested on many real problems (up to 10 dimensions) from computational and cognitive neuroscience, with and without likelihoods. Our method performed consistently well in reconstructing the ground-truth posterior and model evidence with a limited budget of evaluations, showing promise as a general tool for black-box, sample-efficient approximate inference — with exciting potential extensions to more complex cases.

**24/11, Peter Jagers and Sergey Zuyev, Chalmers: Galton was right: all populations die out**Abstract. The frequent extinction of populations (families, species,….) constitutes a classical scientific problem. In 1875 Francis Galton and Henry Watson introduced the Galton-Watson process and claimed that they proved the extinction of all families within its framework. Their proof contained a now famous, but for 50 years undetected, gap: for branching type processes (i.e. populations where individuals reproduce in an i.i.d. style fashion) the real truth is a dichotomy between extinction and exponential growth. However, as we proved recently (J. Math. Biol. 2020), if populations turn subcritical whenever they exceed a carrying capacity, then they must die out, under natural (almost self-evident) conditions. This however may take its time, if the carrying capacity is large.

Mathematically, the proof relies upon local supermartingales and Doob’s maximal inequality.

**1/12, Umberto Simola, University of Helsinki: Adaptive Approximate Bayesian Computation Tolerance Selection**Abstract: Approximate Bayesian Computation (ABC) methods are increasingly used for inference in situations in which the likelihood function is either computationally costly or intractable to evaluate. Extensions of the basic ABC rejection algorithm have improved the computational efficiency of the procedure and broadened its applicability. The ABC-Population Monte Carlo (ABC-PMC) approach has become a popular choice for approximate sampling from the posterior. ABC-PMC is a sequential sampler with an iteratively decreasing value of the tolerance, which species how close the simulated data need to be to the real data for acceptance. We propose a method for adaptively selecting a sequence of tolerances that improves the computational efficiency of the algorithm over other common techniques. In addition we define a stopping rule as a by-product of the adaptation procedure, which assists in automating termination of sampling. The proposed automatic ABC-PMC algorithm can be easily implemented and we present several examples demonstrating its benefits in terms of computational efficiency.

**8/12, Magnus Röding, Chalmers and RISE: Mass transport in porous materials – combining physics, spatial statistics, machine learning, and data science**

Abstract: The three-dimensional microstructure of materials has a significant impact on their performance. Thus, learning how to optimize a 3D microstructure for high performance in a particular application is a core aim of contemporary materials science. Increasingly, exploration of candidate materials is performed computationally, "in silico", which is much cheaper and faster than experimental investigation. This paradigm has already had implications on the development of many types of materials in catalysis, filtration and separation, energy, fuels, and electrochemistry, hygiene products, pharmaceutics, packaging, etc. In several projects, we study the relationships between the microscopic structure of porous materials and their mass transport properties, e.g. diffusion and fluid transport through the pore space. This is done using a multitude of methods: First, realistic mathematical models for materials need to be developed, using different methods from spatial statistics. Second, high-performance solvers for diffusion and flow equations are needed. Third, statistical measures to characterize the microstructure are needed to relate the pore space geometry to the properties of the material. Fourth, to understand the relationships, we utilize analytical, physical models as well as machine learning and data science. In this talk, we illustrate how the combination of different methods lead to better understanding of materials, their microstructures, and their properties.

## 2019

**24/1 - Mats Gyllenberg, Helsingfors Universitet: On models of physiologically structured populations and their reduction to ordinary differential equations**

Sammanfattning: Considering the environmental condition as a given function of time, we formulate a physiologically structured population model as a linear non-autonomous integral equation for the, in general distributed, population level birth rate. We take this renewal equation as the starting point for addressing the following question: When does a physiologically structured population model allow reduction to an ODE without loss of relevant information? We formulate a precise condition for models in which the state of individuals changes deterministically, that is, according to an ODE. Specialising to a one-dimensional individual state, like size, we present various sufficient conditions in terms of individual growth-, death-, and reproduction rates, giving special attention to cell fission into two equal parts and to the catalogue derived in an other paper of ours (submitted). We also show how to derive an ODE system describing the asymptotic large time behaviour of the population when growth, death and reproduction all depend on the environmental condition through a common factor (so for a very strict form of physiological age).

**31/1 - Christian A. Naesseth, Automatic Control, Linköping: Variational and Monte Carlo methods - Bridging the Gap**

Abstract: Many recent advances in large scale probabilistic inference rely on the combination of variational and Monte Carlo (MC) methods. The success of these approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior. My aim is to show how MC methods can be used not only for stochastic optimization of the variational parameters, but also for defining a more flexible parametric approximation in the first place. First, I will review variational inference (VI). Second, I describe some of the pivotal tools for VI, based on MC methods and stochastic optimization, that have been developed in the last few years. Finally, I will show how we can synthesize sequential Monte Carlo methods and VI to learn more accurate posterior approximations with theoretical guarantees.

**7/2 - Jonas Wallin, Lund University: Multivariate Type-G Matérn fields**

Abstract: I will present a class of non-Gaussian multivariate random fields is formulated using systems of stochastic partial differential equations (SPDEs) with additive non-Gaussian noise. To facilitate computationally efficient likelihood-based inference, the noise is constructed using normal-variance mixtures (type-G noise). Similar, but simpler, constructions have been proposed earlier in the literature, however they lack important properties such as ergodicity and flexibility of predictive distributions. I will present that for a specific system of SPDEs the marginal of the fields has Matérn covariance functions.

Further I will present a parametrization of the system, that one can use to separate the cross-covariance and the extra dependence coming from the non-Gaussian noise in the proposed model.

If time permits I will discuss some recent result on proper scoring rules (PS). PS is the standard tool for evaluating which model fits data best in spatial statistics (like Gaussian vs non-Gaussian models).

We have developed a new class of PS that I argue is better suited for evaluation model if one has observations at irregular locations.

**14/2 - Jes Frellsen, IT University of Copenhagen: Deep latent variable models: estimation and missing data imputation**

Abstract: Deep latent variable models (DLVMs) combine the approximation abilities of deep neural networks and the statistical foundations of generative models. In this talk, we first give a brief introduction to deep learning. Then we discuss how DLVMs are estimated: variational methods are commonly used for inference; however, the exact likelihood of these models has been largely overlooked. We show that most unconstrained models used for continuous data have an unbounded likelihood function and discuss how to ensure the existence of maximum likelihood estimates. Then we present a simple variational method, called MIWAE, for training DLVMs, when the training set contains missing-at-random data. Finally, we present Monte Carlo algorithms for missing data imputation using the exact conditional likelihood of DLVMs: a Metropolis-within-Gibbs sampler for DLVMs trained on complete datasets and an importance sampler for DLVMs trained on incomplete data sets. For complete training sets, our algorithm consistently and significantly outperforms the usual imputation scheme used for DLVMs. For incomplete training set, we show that MIWAE trained models provide accurate single and multiple imputations, and are highly competitive with state-of-the-art methods.

This is joint work with Pierre-Alexandre Mattei.

Abstract: Influential points can cause severe problems when deriving a multivariable regression model. A novel approach to check for such points is proposed, based on the variable inclusion matrix, a simple way to summarize results from resampling-based variable selection procedures. These procedures rely on the variable inclusion matrix, which reports whether a variable (column) is included in a regression model fitted on a pseudo-sample (row) generated from the original data (e.g., bootstrap sample or subsample). The variable inclusion matrix is used to study the variable selection stability, to derive weights for model averaged predictors and in others investigations. Concentrating on variable selection, it also allows understanding whether the presence of a specific observation has an influence on the selection of a variable.

From the variable inclusion matrix, indeed, the inclusion frequency (I-frequency) of each variable can be computed only in the pseudo-samples (i.e., rows) which contain the specific observation. When the procedure is repeated for each observation, it is possible to check for influential points through the distribution of the I-frequencies, visualized in a boxplot, or through a Grubbs’ test. Outlying values in the former case and significant results in the latter point to observations having an influence on the selection of a specific variable and therefore on the finally selected model. This novel approach is illustrated in two real data examples.

This is joint work with Pierre-Alexandre Mattei.

**21/2 - Riccardo De Bin, University of Oslo: Detection of influential points as a byproduct of resampling-based variable selection procedures**Abstract: Influential points can cause severe problems when deriving a multivariable regression model. A novel approach to check for such points is proposed, based on the variable inclusion matrix, a simple way to summarize results from resampling-based variable selection procedures. These procedures rely on the variable inclusion matrix, which reports whether a variable (column) is included in a regression model fitted on a pseudo-sample (row) generated from the original data (e.g., bootstrap sample or subsample). The variable inclusion matrix is used to study the variable selection stability, to derive weights for model averaged predictors and in others investigations. Concentrating on variable selection, it also allows understanding whether the presence of a specific observation has an influence on the selection of a variable.

From the variable inclusion matrix, indeed, the inclusion frequency (I-frequency) of each variable can be computed only in the pseudo-samples (i.e., rows) which contain the specific observation. When the procedure is repeated for each observation, it is possible to check for influential points through the distribution of the I-frequencies, visualized in a boxplot, or through a Grubbs’ test. Outlying values in the former case and significant results in the latter point to observations having an influence on the selection of a specific variable and therefore on the finally selected model. This novel approach is illustrated in two real data examples.

**28/2 - Johan Henriksson: Single-cell perturbation analysis – the solution to systems biology?**Abstract: The ideas behind systems biology has been around for ages. However, the field has been held back by the lack of data. In this talk I will cover new methods, by me and others, toward generating the large amounts of data needed to fit realistic regulatory models. Focus will be on wet lab methods as well as equations, and how we practically can solve them. I will try to cover, in particular, CRISPR, RNA-seq, ATAC-seq, STARR-seq, bayesian models, ODE and a bit of physics.

**7/3 - Larisa Beilina: Time-adaptive parameter identification in mathematical model of HIV infection with**

**drug therapy**

Abstract: Parameter identification problems are frequently occurring within biomedical applications. These problems are often ill-posed, and thus challenging to solve numerically. In this talk will be presented the time-adaptive optimization method for determination of drug efficacy in the mathematical model of HIV infection. Time-adaptive method means that first we determine drug efficacy at known coarse time partition using known values of observed functions. Then we locally refine time-mesh at points where a posteriori error indicator is large and compute drug efficacy on a new refined mesh until the error is reduced to the desired accuracy. The time-adaptive method can eventually be used by clinicians to determine the drug-response for each treated individual. The exact knowledge of the personal drug efficacy can aid in the determination of the most suitable drug as well as the most optimal dose for each person, in the long run resulting in a personalized treatment with maximum efficacy and minimum adverse drug reactions.

**14/3 - Umberto Picchini: Accelerating MCMC sampling via approximate delayed-acceptance**Abstract: While Markov chain Monte Carlo (MCMC) is the ubiquitous tool for sampling from complex probability distributions, it does not scale well with increasing datasets. Also, its structure is not naturally suited for parallelization.

When pursuing Bayesian inference for model parameters, MCMC can be computationally very expensive, either when the dataset is large, or when the likelihood function is unavailable in closed form and itself requires Monte Carlo approximations. In these cases each iteration of Metropolis-Hastings may result intolerably slow. The so-called "delayed acceptance" MCMC (DA-MCMC) was suggested by Christen and Fox in 2005 and allows the use of a computationally cheap surrogate of the likelihood function to rapidly screen (and possibly reject) parameter proposals, while using the expensive likelihood only when the proposal has survived the "scrutiny" of the cheap surrogate. They show that DA-MCMC samples from the exact posterior distribution and returns results much more

rapidly than standard Metropolis-Hastings. Here we design a novel delayed-acceptance algorithm, which is between 2 and 4 times faster than the original DA-MCMC, though ours results in approximate inference. Despite this, we show empirically that our algorithm returns accurate inference. A computationally intensive case study is discussed,

involving ~25,000 observations from protein folding reaction coordinate, fit by an SDE model with an intractable likelihood approximated using sequential Monte Carlo (that is particle MCMC).

This is joint work with Samuel Wiqvist, Julie Lyng Forman, Kresten Lindorff-Larsen and Wouter Boomsma.

keywords: Bayesian inference, Gaussian process; intractable likelihood; particle MCMC; protein folding; SDEs

When pursuing Bayesian inference for model parameters, MCMC can be computationally very expensive, either when the dataset is large, or when the likelihood function is unavailable in closed form and itself requires Monte Carlo approximations. In these cases each iteration of Metropolis-Hastings may result intolerably slow. The so-called "delayed acceptance" MCMC (DA-MCMC) was suggested by Christen and Fox in 2005 and allows the use of a computationally cheap surrogate of the likelihood function to rapidly screen (and possibly reject) parameter proposals, while using the expensive likelihood only when the proposal has survived the "scrutiny" of the cheap surrogate. They show that DA-MCMC samples from the exact posterior distribution and returns results much more

rapidly than standard Metropolis-Hastings. Here we design a novel delayed-acceptance algorithm, which is between 2 and 4 times faster than the original DA-MCMC, though ours results in approximate inference. Despite this, we show empirically that our algorithm returns accurate inference. A computationally intensive case study is discussed,

involving ~25,000 observations from protein folding reaction coordinate, fit by an SDE model with an intractable likelihood approximated using sequential Monte Carlo (that is particle MCMC).

This is joint work with Samuel Wiqvist, Julie Lyng Forman, Kresten Lindorff-Larsen and Wouter Boomsma.

keywords: Bayesian inference, Gaussian process; intractable likelihood; particle MCMC; protein folding; SDEs

**21/3 - Samuel Wiqvist, Lund University: Automatic learning of summary statistics for Approximate Bayesian Computation using Partially Exchangeable Networks**Abstract: Likelihood-free methods enable statistical inference for the parameters of complex models, when the likelihood function is analytically intractable. For these models, several tools are available that only require the ability to run a computer simulator of the mathematical model, and use the output to replace the unavailable likelihood function. The most famous of these type of methodologies is Approximate Bayesian Computation (ABC), which relies on the access to low-dimensional summary statistics of the data. Learning these summary statistics is a fundamental problem in ABC, and selecting them is not trivial. It is in fact the main challenge when applying ABC in practice, and it affects the resulting inference considerably. Deep learning methods have previously been used to learn summary statistics for ABC.

Here we introduce a novel deep learning architecture (Partially Exchangeable Networks, PENs), with the purpose to automatize the summaries selection task. We only need to provide our network with samples from the prior predictive distribution, and this will return summary statistics for ABC use. PENs are designed to have the correct invariance property for Markovian data, and PENs are therefore particularly useful when learning summary statistics for Markovian data.

Case studies show that our methodology outperforms other popular methods, resulting in more accurate ABC inference for models with intractable likelihoods. Empirically, we show that for some case studies our approach seems to work well also with non-Markovian and non-exchangeable data.

Here we introduce a novel deep learning architecture (Partially Exchangeable Networks, PENs), with the purpose to automatize the summaries selection task. We only need to provide our network with samples from the prior predictive distribution, and this will return summary statistics for ABC use. PENs are designed to have the correct invariance property for Markovian data, and PENs are therefore particularly useful when learning summary statistics for Markovian data.

Case studies show that our methodology outperforms other popular methods, resulting in more accurate ABC inference for models with intractable likelihoods. Empirically, we show that for some case studies our approach seems to work well also with non-Markovian and non-exchangeable data.

**28/3 -****Hans Falhlin (****Chief Investment Officer,****AP2, Andra AP-fonden)****and Tomas Morsing (****Head of Quantitative Strategies,****AP2, Andra AP-fonden):****A scientific approach to financial decision making****in the context of managing Swedish pension assets**Abstract: The Second Swedish Pension Fund AP2 is one of the four large Swedish pension buffer funds. In this presentation we will give examples of our scientific approach to financial decision making in the area of strategic asset allocation and, in greater depth, model based portfolio management. Model based portfolio management, the management of portfolios of financial assets with mathematical and statistical models, involve many interesting and challenging problems. We will in this presentation give an overview of the area and indicate areas for future research.

Abstract: Our planet and its long history are characterized by a stunning diversity of organisms, environments and, more recently, cultures and technologies. To understand what factors contribute to generating diversity and shaping its evolution we have to look beyond diversity patterns. Here I present a suite of Bayesian models to infer the dynamics of origination and extinction processes using fossil occurrence data and show how the models can be adapted to the study of cultural evolution. Through empirical examples, I will demonstrate the use of this probabilistic framework to test specific hypotheses and quantify the processes underlying (bio)diversity patterns and their evolution.

Abstract: In this talk, we study the persistent homology and related geometric properties of the evolution in time of a discrete-time stochastic process defined on the 2-dimensional regular square lattice. This process corresponds to a cell growth model called the Eden Growth Model (EGM). It can be described as follows: start with the cell square of the 2-dimensional regular square lattice of the plane that contains the origin; then make the cell structure grow by adding one cell at each time uniformly random to the perimeter. We give a characterization of the possible change in the rank of the first homology group of this process (the "number of holes"). Based on this result we have designed and implemented a new algorithm that computes the persistent homology associated to this stochastic process and that also keeps track of geometric features related to the homology. Also, we present obtained results of computational experiments performed with this algorithm, and we establish conjectures about the asymptotic behaviour of the homology and other related geometric random variables. The EGM can be seen as a First Passage Percolation model after a proper time-scaling. This is the first time that tools and techniques from stochastic topology and topological data analysis are used to measure the evolution of the topology of the EGM and in general in FPP models.

**11/4 - Daniele Silvestro: Birth-death models to understand the evolution of (bio)diversity**Abstract: Our planet and its long history are characterized by a stunning diversity of organisms, environments and, more recently, cultures and technologies. To understand what factors contribute to generating diversity and shaping its evolution we have to look beyond diversity patterns. Here I present a suite of Bayesian models to infer the dynamics of origination and extinction processes using fossil occurrence data and show how the models can be adapted to the study of cultural evolution. Through empirical examples, I will demonstrate the use of this probabilistic framework to test specific hypotheses and quantify the processes underlying (bio)diversity patterns and their evolution.

**12/4 - Erika B. Roldan Roa, Department of Mathematics, The Ohio State University: Evolution of the homology and related geometric properties of the Eden Growth Model**Abstract: In this talk, we study the persistent homology and related geometric properties of the evolution in time of a discrete-time stochastic process defined on the 2-dimensional regular square lattice. This process corresponds to a cell growth model called the Eden Growth Model (EGM). It can be described as follows: start with the cell square of the 2-dimensional regular square lattice of the plane that contains the origin; then make the cell structure grow by adding one cell at each time uniformly random to the perimeter. We give a characterization of the possible change in the rank of the first homology group of this process (the "number of holes"). Based on this result we have designed and implemented a new algorithm that computes the persistent homology associated to this stochastic process and that also keeps track of geometric features related to the homology. Also, we present obtained results of computational experiments performed with this algorithm, and we establish conjectures about the asymptotic behaviour of the homology and other related geometric random variables. The EGM can be seen as a First Passage Percolation model after a proper time-scaling. This is the first time that tools and techniques from stochastic topology and topological data analysis are used to measure the evolution of the topology of the EGM and in general in FPP models.

**16/5 - Susanne Ditlevsen, University of Copenhagen: Inferring network structure from oscillating systems with cointegrated phase processes**We present cointegration analysis as a method to infer the network structure of a linearly phase coupled oscillating system. By defining a class of oscillating systems with interacting phases, we derive a data generating process where we can specify the coupling structure of a network that resembles biological processes. In particular we study a network of Winfree oscillators, for which we present a statistical analysis of various simulated networks, where we conclude on the coupling structure: the direction of feedback in the phase processes and proportional coupling strength between individual components of the system. We show that we can correctly classify the network structure for such a system by cointegration analysis, for various types of coupling, including uni-/bi-directional and all-to-all coupling. Finally, we analyze a set of EEG recordings and discuss the current applicability of cointegration analysis in the field of neuroscience.

Ref: J. Østergaard, A. Rahbek and S. Ditlevsen. Oscillating systems with cointegrated phase processes. Journal of Mathematical Biology, 75(4), 845--883, 2017.

Abstract: Since its introduction in the context of communication theory, information theory has extended to a wide range of disciplines in both natural and social sciences. In this talk, I will explore information theory as a nonparametric probabilistic framework for unsupervised and supervised learning free from a prioriassumption on the underlying statistical model. In particular, the soft (fuzzy) clustering problem in unsupervised learning can be viewed as a tradeoff between data compression and minimizing the distortion of the data. Similarly, modeling in supervised learning can be treated as a tradeoff between compression of the predictor variables and retaining the relevant information about the response variable. To illustrate the usage of these methods, some applications in biophysical problems and time series analysis will be briefly addressed in the talk.

**23/5 - Chun-Biu Li, Stockholms Universitet: Information Theoretic Approaches to Statistical Learning**Abstract: Since its introduction in the context of communication theory, information theory has extended to a wide range of disciplines in both natural and social sciences. In this talk, I will explore information theory as a nonparametric probabilistic framework for unsupervised and supervised learning free from a prioriassumption on the underlying statistical model. In particular, the soft (fuzzy) clustering problem in unsupervised learning can be viewed as a tradeoff between data compression and minimizing the distortion of the data. Similarly, modeling in supervised learning can be treated as a tradeoff between compression of the predictor variables and retaining the relevant information about the response variable. To illustrate the usage of these methods, some applications in biophysical problems and time series analysis will be briefly addressed in the talk.

**13/6 - Sara Hamis, Swansea University: DNA Damage Response Inhibition: Predicting in vivo treatment responses using an in vitro- calibrated mathematical model**Abstract: Mathematical models, and their corresponding in silico experiments, can be used to simulate both in vitro and in vivo tumour scenarios. However, the microenvironment in an in vitro cell culture is significantly different from the microenvironment in a solid tumour and many details that influence tumour dynamics differ between in vitro and in vivo settings. These details include cell proliferation, oxygen distribution and drug delivery. It follows that translating quantitative in vitro findings to in vivo predictions is not straightforward.

In this talk I will present an individual based mathematical cancer model in which one individual corresponds to one cancer cell. This model is governed by a few observable and well documented principles, or rules. To account for differences between the in vitro and in vivo scenarios, these rules can be appropriately adjusted. By only adjusting the rules (whilst keeping the fundamental framework intact), the mathematical model can first be calibrated by in vitro data and thereafter be used to successfully predict treatment responses in mouse xenografts in vivo. The model is used to investigate treatment responses to a drug that hinders tumour proliferation by targeting the cellular DNA damage response process.

In this talk I will present an individual based mathematical cancer model in which one individual corresponds to one cancer cell. This model is governed by a few observable and well documented principles, or rules. To account for differences between the in vitro and in vivo scenarios, these rules can be appropriately adjusted. By only adjusting the rules (whilst keeping the fundamental framework intact), the mathematical model can first be calibrated by in vitro data and thereafter be used to successfully predict treatment responses in mouse xenografts in vivo. The model is used to investigate treatment responses to a drug that hinders tumour proliferation by targeting the cellular DNA damage response process.

**19/9 - Ronald Meester, Vrije University, Amsterdam: The DNA Database Controversy 2.0**Abstract: What is the evidential value of a unique match of a DNA profile in database? Although the probabilistic analysis of this problem is in principle not difficult, it was the subject of a heated debate in the literature around 15 years ago, to which I also contributed. Very recently, to my surprise, the debate was re-opened by the publication of a paper by Wixted, Christenfeld and Rouder, in which a new element to the discussion was introduced. They claimed that the size of the criminal population (however defined) was important. In this lecture I will first review the database problem, together with the principal solution. Then I explain why this new ingredient does not add anything, and only obscures the picture. The fact that not everybody agrees with us will be illustrated by some interesting quotes from the recent literature. If you thought that mathematics could not be polemic you should certainly come and listen. (Joint work with Klaas Slooten.)

**26/9 - Valerie Monbet, Université de Rennes: Time-change models for asymmetric processes**Many records in environmental sciences exhibit asymmetric trajectories. The physical mechanisms behind these records may lead for example to sample paths with different characteristics at high and low levels (up-down asymmetries) or in the ascending and descending phases leading to time irreversibility (front-back asymmetries). Such features are important for many applications and there is a need for simple and tractable models which can reproduce them. We explore original time-change models where the clock is a stochastic process which depends on the observed trajectory. The ergodicity of the proposed model is established under general conditions and this result is used to develop non-parametric estimation procedures based on the joint distribution of the process and its derivative. The methodology is illustrated on meteorological and oceanographic datasets. We show that, combined with a marginal transformation, the proposed methodology is able to reproduce important characteristics of the dataset such as marginal distributions, up-crossing intensity, up-down and front-back asymmetries.

**3/10 - Peter Jagers, Chalmers: Populations - from few independently reproducing individuals to continuous and deterministic flows. Or: From branching processes to adaptive population dynamics**Abstract: When the density of populations grows, in pace with an environmental carrying capacity growth, general branching populations with interacting individuals and also in interplay with the environment, will stabilise towards a deterministic population flow, determined by an integral equation. The deviation between the original density and the limiting one, as the carrying capacity grows beyond all limits, will also converge to a diffusion process. This provides a firm basis in individual behaviour for ad hoc deterministic population models.

**17/10 - Richard Davis, Columbia University and Chalmers Jubileum Professor 2019: Extreme Value Theory Without the Largest Values: What Can Be Done?**Abstract: During the last five years, there has been growing interest in inference related problems in the traditional extreme value theory setup in which the data has been truncated above some large value. The principal objectives have been to estimate the parameters of the model, usually in a Pareto or a generalized Pareto distribution (GPD) formulation, together with the truncated value. Ultimately, the Hill estimator plays a starring role in this work. In this paper we take a different perspective. Motivated by data coming from a large network, the Hill estimator appeared to exhibit smooth “sample path” behavior as a function of the number of upper order statistics used in the constructing the estimator. This became more apparent as we artificially censored more of the upper order statistics. Building on this observation, we introduce a new parameterization into the Hill estimator that is a function of δ and θ, that correspond, respectively, to the proportion of extreme values that have been censored and the path behavior of the “Hill estimator”. As a function of (δ,θ), we establish functional convergence of the renormalized Hill estimator to a Gaussian process. Based on this limit theory, an estimation procedure is developed to estimate the number of censored observations and other extreme value parameters including $\alpha$, the index of regular variation and the bias of Hill’s estimate. We illustrate this approach in both simulations and with real data. (This is joint work with Jingjing Zou and Gennady Samorodnitsky.)

**24/10 - Erica Metheney, Department of Political Sciences, University of Gothenburg: Modifying Non-Graphic Sequences to be Graphic**Abstract: The field of network science has expanded greatly in recent years with applications in fields such as computer science, biology, chemistry, and political science. Overtime the networks in which we are interested have become larger and more interconnected, posing new computational challenges. We study the generation of graphic degree sequences in order to improve the overall efficiency of simulating networks with power-law degree distributions. We explain the challenges associated with this class of networks and present an algorithm to modify non-graphic degree sequences to be graphic. Lastly we show that this algorithm preserves the original degree distribution and satisfies certain optimality properties.

**31/10 - Sofia Tapani, AstraZeneca: Early clinical trial design - Platform designs with the patient at its center**Abstract text: Adapting a portfolio approach to the implementation of clinical trials at the early stage has been evaluated within the oncology therapy area.

This feature of clinical trial design can also add value to other therapy areas due to its potential exploratory nature. The platform design allows for multi-arm clinical trials to evaluate several experimental treatments perhaps not all available at the same point in time. At the early clinical development stage, new drugs are rarely at the same stage of development. The alternative, several separate two-arm studies is time consuming and can be a bottle neck in development due to budget limitations in comparison to the more efficient platform study where arms are added at several different time points after start of enrolment.

Platform designs within the heart failure therapy area in early clinical development are exploratory of nature. Clear prognostic and predictive biomarker profiles for disease are not available and need to be explored to be identified for each patient population. As an example, we’ll have a look at the HIDMASTER trial design for biomarker identification and compound graduation throughout the platform.

All platform trials need to be thoroughly simulated, and simulations should be used as a tool to decide among design options. Simulations of platform trials gives the opportunity to investigate many scenarios including null scenario to establish overall type I error. We can evaluate bias estimation and sensitivity to patient withdrawals, missing data, enrolment rates/patterns, interim analysis timings, data access delays, data cleanliness, analysis delays, etc.

Simulations should also comprise decision operating characteristics to be able to make decisions on the design based on the objective of the trial: early stops of underperforming arms, early go for active arms, prioritise arms on emerging data or drawing insights from whole study data analysis.

Over time the trial learns about the disease, new endpoints, stratification biomarkers and prognostic vs predictive effects.

This feature of clinical trial design can also add value to other therapy areas due to its potential exploratory nature. The platform design allows for multi-arm clinical trials to evaluate several experimental treatments perhaps not all available at the same point in time. At the early clinical development stage, new drugs are rarely at the same stage of development. The alternative, several separate two-arm studies is time consuming and can be a bottle neck in development due to budget limitations in comparison to the more efficient platform study where arms are added at several different time points after start of enrolment.

Platform designs within the heart failure therapy area in early clinical development are exploratory of nature. Clear prognostic and predictive biomarker profiles for disease are not available and need to be explored to be identified for each patient population. As an example, we’ll have a look at the HIDMASTER trial design for biomarker identification and compound graduation throughout the platform.

All platform trials need to be thoroughly simulated, and simulations should be used as a tool to decide among design options. Simulations of platform trials gives the opportunity to investigate many scenarios including null scenario to establish overall type I error. We can evaluate bias estimation and sensitivity to patient withdrawals, missing data, enrolment rates/patterns, interim analysis timings, data access delays, data cleanliness, analysis delays, etc.

Simulations should also comprise decision operating characteristics to be able to make decisions on the design based on the objective of the trial: early stops of underperforming arms, early go for active arms, prioritise arms on emerging data or drawing insights from whole study data analysis.

Over time the trial learns about the disease, new endpoints, stratification biomarkers and prognostic vs predictive effects.

**6/11 - Richard Torkar, Software Engineering, Chalmers: Why do we encourage even more missingness when dealing with missing data?**Abstract: In this presentation, we first introduce the reader to Bayesian data analysis (BDA) and missing data, and, in particular, how this is handled in empirical software engineering (ESE) research today. The example we make use of presents the steps done when conducting state of the art statistical analysis in our field. First, we need to understand the problem we want to solve. Second, we conduct causal analysis. Third, we analyze non-identifiability. Fourth, we conduct missing data analysis. Finally, we do a sensitivity analysis of priors. All this before we design our statistical model. Once we have a model, we present several diagnostics one can use to conduct sanity checks. We hope that through these examples, empirical software engineering will see the advantages of using BDA. This way, we hope Bayesian statistics will become more prevalent in our field, thus partly avoiding the reproducibility crisis we have seen in other disciplines. Our hope is that in this seminar statisticians will provide (valuable!) feedback on what is proposed, and hence provide empirical software engineering with a good first step in using BDA for the type of analyses we conduct.

**7/11 - Krzysztof Bartoszek, Linköping University: Formulating adaptive hypotheses in multivariate phylogenetic comparative methods**Abstract: (joint work with G. Asimomitis, V. Mitov, M. Piwczyński, T. Stadler) Co-adaptation is key to understanding species evolution. Different traits have to function together so that the organism can work as a whole. Hence, all changes to environmental pressures have to be coordinated. Recently, we have developed R packages that are able to handle general, multivariate Gaussian processes realized over a phylogenetic tree. At the heart of the modelling framework is the so-called GLInv (Gaussian, mean depending linearly on the ancestral value and variance Invariant with respect to ancestral value) family of models. More formally a stochastic process evolving on a tree belongs to this family if

* after branching the traits evolve independently

* the distribution of the trait at time t, X(t), conditional on the ancestral value, X(s), at time s<t, is Gaussian with ** E[X(t) | X(s)] =

w(s,t) + F(s,t)X(s)

** Var[X(t) | X(s) ] = V(s,t),

where neither w(s,t), F(s,t), nor V(s,t) can depend on X(.) but may be further parametrized. Using the likelihood computational engine PCMBase [2, available on CRAN] the PCMFit [3, publicly available on GitHub] package allows for inference of models belonging to the GLInv family and furthermore allows for finding points of shifts between evolutionary regimes n the tree. What is particularly novel is that it allows not only for shifts between a model's parameters but for switches between different types of models within then GLInv family (e.g. a shift from a Brownian motion (BM) to an Ornstein-Uhlenbeck (OU) process and vice versa). Interactions between traits can be understood as magnitudes and signs of off-diagonal entries of F(s,t) or V(s,t). What is particularly interesting is that in this family of models one may obtain changes in the direction of the relationship, i.e. the long and short term joint dynamics can be of a different nature. This is possible even if one simplifies the process to an OU one. Here, one is able to very finely understand the dynamics of the process and propose specific model parameterizations [PCMFit and current CRAN version of mvSLOUCH, 1, which is based on PCMBase]. In the talk I will discuss how one can setup different hypotheses concerning relationships between the traits in terms of model parameters and how one can view the long and short term evolutionary dynamics. The software's possibilities will be illustrated by considering the evolution of fruit in the Ferula genus. I will also discuss some limit results that are amongst others, useful for setting initial seeds of the numerical estimation procedures.

* after branching the traits evolve independently

* the distribution of the trait at time t, X(t), conditional on the ancestral value, X(s), at time s<t, is Gaussian with ** E[X(t) | X(s)] =

w(s,t) + F(s,t)X(s)

** Var[X(t) | X(s) ] = V(s,t),

where neither w(s,t), F(s,t), nor V(s,t) can depend on X(.) but may be further parametrized. Using the likelihood computational engine PCMBase [2, available on CRAN] the PCMFit [3, publicly available on GitHub] package allows for inference of models belonging to the GLInv family and furthermore allows for finding points of shifts between evolutionary regimes n the tree. What is particularly novel is that it allows not only for shifts between a model's parameters but for switches between different types of models within then GLInv family (e.g. a shift from a Brownian motion (BM) to an Ornstein-Uhlenbeck (OU) process and vice versa). Interactions between traits can be understood as magnitudes and signs of off-diagonal entries of F(s,t) or V(s,t). What is particularly interesting is that in this family of models one may obtain changes in the direction of the relationship, i.e. the long and short term joint dynamics can be of a different nature. This is possible even if one simplifies the process to an OU one. Here, one is able to very finely understand the dynamics of the process and propose specific model parameterizations [PCMFit and current CRAN version of mvSLOUCH, 1, which is based on PCMBase]. In the talk I will discuss how one can setup different hypotheses concerning relationships between the traits in terms of model parameters and how one can view the long and short term evolutionary dynamics. The software's possibilities will be illustrated by considering the evolution of fruit in the Ferula genus. I will also discuss some limit results that are amongst others, useful for setting initial seeds of the numerical estimation procedures.

[1] K. Bartoszek, J. Pienaar, P. Mostad, S. Andersson, and T. F. Hansen.

A phylogenetic comparative method for studying multivariate adaptation.

J. Theor. Biol. 314:204-215, 2012.

[2] V. Mitov, K. Bartoszek, G. Asimomitis, T. Stadler. Fast likelihood calculation for multivariate phylogenetic comparative methods: The PCMBase R package. arXiv:1809.09014, 2018.

[3] V. Mitov, K. Bartoszek, T. Stadler. Automatic generation of evolutionary hypotheses using mixed Gaussian phylogenetic models. PNAS, 201813823, 2019.

A phylogenetic comparative method for studying multivariate adaptation.

J. Theor. Biol. 314:204-215, 2012.

[2] V. Mitov, K. Bartoszek, G. Asimomitis, T. Stadler. Fast likelihood calculation for multivariate phylogenetic comparative methods: The PCMBase R package. arXiv:1809.09014, 2018.

[3] V. Mitov, K. Bartoszek, T. Stadler. Automatic generation of evolutionary hypotheses using mixed Gaussian phylogenetic models. PNAS, 201813823, 2019.

**20/11 - Paul-Christian Bürkner, Aalto University: Bayesflow: Software assisted Bayesian workflow**

Abstract: Probabilistic programming languages such as Stan, which can be used to specify and fit Bayesian models, have revolutionized the practical application of Bayesian statistics. They are an integral part of Bayesian data analysis and as such, a necessity to obtain reliable and valid inference. However, they are not sufficient by themselves. Instead, they have to be combined with substantive statistical and subject matter knowledge, expertise in programming and data analysis, as well as critical thinking about the decisions made in the process.

A principled Bayesian workflow consists of several steps from the design of the study, gathering of the data, model building, estimation, and validation, to the final conclusions about the effects under study. I want to present a concept for a software package that assists users in following a principled Bayesian workflow for their data analysis by diagnosing problems and giving recommendations for sensible next steps. This concept gives rise to a lot of interesting research questions we want to investigate in the upcoming years.

A principled Bayesian workflow consists of several steps from the design of the study, gathering of the data, model building, estimation, and validation, to the final conclusions about the effects under study. I want to present a concept for a software package that assists users in following a principled Bayesian workflow for their data analysis by diagnosing problems and giving recommendations for sensible next steps. This concept gives rise to a lot of interesting research questions we want to investigate in the upcoming years.

**27/11 - Geir Storvik, Oslo University: Flexible Bayesian Nonlinear Model Configuration**Abstract: Deep learning models have been extremely successful in terms of prediction although they are often difficult to specify and potentially suffer from overfitting. In this talk, we introduce the class of Bayesian generalized nonlinear regression models (BGNLM) with a comprehensive non-linear feature space. Non-linear features are generated hierarchically similarly to deep learning, but with extended flexibility on the possible types of features to be considered. This extended flexibility combined with variable selection allows to find a small set of important features and thereby more interpretable models. A mode jumping MCMC algorithm is presented to make inference on BGNLMs. Model averaging is also possible within our framework. In various applications, we illustrate how BGNLM is used to obtain meaningful non-linear models. Additionally, we compare its predictive performance with a number of machine learning algorithms.

This is joint work with Aliaksandr Hubin (Norwegian Computing Center) and Florian Frommlet (CEMSIIS, Medical University of Vienna)

This is joint work with Aliaksandr Hubin (Norwegian Computing Center) and Florian Frommlet (CEMSIIS, Medical University of Vienna)

**4/12 - Moritz Schauer, Chalmers/GU: Smoothing and inference for high dimensional diffusions**Abstract: Suppose we discretely observe a diffusion process and we wish to estimate parameters appearing in either the drift coefficient or the diffusion coefficient. We derive a representation of the conditional distribution given observations as change of measure to be embedded as a step in a Monte-Carlo procedure to estimate those parameters. The technique is based on solving the reverse time filtering problem for a linear approximation of the diffusion and a change of measure to correct for the difference between the linear approximation and the true smoothed process.

We apply this to the problem of tracking convective cloud systems from satellite data with low time resolution.

We apply this to the problem of tracking convective cloud systems from satellite data with low time resolution.

**11/12 - Johannes Borgqvist, Chalmers/GU: The polarising world of Cdc42: the derivation and analysis of a quantitative reaction diffusion model of cell polarisation**Abstract: A key regulator of cell polarisation in organisms ranging from yeast to higher mammals is the Cell division control protein 42 homolog, Cdc42. It is a GTPase of the Rho family which determines the site of the pole by a combination of reactions (i.e. activation and deactivation) and diffusion in the cell. A study in yeast showed that with high age, the Cdc42 pathway loses its function which prevents replicative ageing. Moreover, Cdc42 activity is involved in both ageing and rejuvenation of hematopoietic stem cells which illustrates the importance of Cdc42 in the ageing process of numerous organisms. Experimentally, the challenge is that the concentration profile of Cdc42 is not uniform. Thus, accounting for spatial inhomogeneities is crucial when data is collected, but these experiments are hard to conduct. Similarly, the problem with the numerous mathematical models is that they do not account for cell geometry. Consequently, they do not provide a realistic description of the polarisation process mediated by Cdc42.

In this project, we develop a quantifiable model of cell polarisation accounting for the morphology of the cell. The model consists of a coupled system of PDEs, more specifically Reaction Diffusion equations, with two spatial domains: the cytosol and the cell membrane. In this setting, we prove sufficient conditions for pattern formation. Using a “Finite Element”-based numerical scheme, we simulate cell polarisation for these two domains. Further, we illustrate the impact of the parameters on the patterns that emerge and we estimate the time until polarization. Using this work as a starting point, it is possible to integrate data into the theoretical description of the process to deeper understand cell polarisation mechanistically.

In this project, we develop a quantifiable model of cell polarisation accounting for the morphology of the cell. The model consists of a coupled system of PDEs, more specifically Reaction Diffusion equations, with two spatial domains: the cytosol and the cell membrane. In this setting, we prove sufficient conditions for pattern formation. Using a “Finite Element”-based numerical scheme, we simulate cell polarisation for these two domains. Further, we illustrate the impact of the parameters on the patterns that emerge and we estimate the time until polarization. Using this work as a starting point, it is possible to integrate data into the theoretical description of the process to deeper understand cell polarisation mechanistically.

## 2018

**24/5 - Erwan Koch (EPFL): Spatial risk measures induced by powers of max-stable random fields**

A meticulous assessment of the risk of extreme environmental events is of great necessity for populations, civil authorities as well as the insurance/reinsurance industry. Koch (2017, 2018) introduced a concept of spatial risk measure and a related set of axioms which are well-suited to analyse and quantify the risk due to events having a spatial extent, precisely such as natural disasters. In this paper, we first carry out a detailed study of the correlation (and covariance) structure of powers of the Smith and Brown-Resnick max-stable random fields. Then, using the latter results, we thoroughly investigate spatial risk measures associated with variance and induced by powers of max-stable random fields. In addition, we show that spatial risk measures associated with several classical risk measures and induced by such cost fields satisfy (at least) part of the previously mentioned axioms under appropriate conditions on the max-stable fields. Considering such cost fields is particularly relevant when studying the impact of extreme wind speeds on buildings and infrastructure.

Key words: Powers of max-stable random fields; Spatial dependence; Spatial diversification; Spatial risk measures and corresponding axioms; Wind damage.

The corresponding paper is available at

https://arxiv.org/pdf/1804.05694.pdf

https://arxiv.org/pdf/1804.05694.pdf

References in the abstract:

- Koch, E. (2017). Spatial risk measures and applications to max-stable processes. Extremes, 20(3):635-670.

- Koch, E. (2018). Spatial risk measures and rate of spatial diversification. Available at https://arxiv.org/abs/1803.07041

- Koch, E. (2017). Spatial risk measures and applications to max-stable processes. Extremes, 20(3):635-670.

- Koch, E. (2018). Spatial risk measures and rate of spatial diversification. Available at https://arxiv.org/abs/1803.07041

**6/9 - Lukas Käll (KTH Genteknologi, SciLifeLab): Distillation of label-free quantitative mass spectrometry data by clustering and Bayesian modeling**

Abstract: Protein quantification by label-free shotgun proteomics experiments is complicated by a multitude of error sources. Typical pipelines for identifying differentially expressed proteins use intermediate filters in an attempt to control the error rate. However, they often ignore certain error sources and, moreover, regard filtered lists as completely correct in subsequent steps. These two indiscretions can easily lead to a loss of control of the false discovery rate (FDR). We propose a probabilistic graphical model, Triqler, that propagates error information through all steps, employing distributions in favour of point estimates, most notably for missing value imputation. The model outputs posterior probabilities for fold changes between treatment groups, highlighting uncertainty rather than hiding it. We will also discuss a method, MaRaQuant, in which we reverse the typical processing workflow into a quantification-first approach. Specifically, we apply unsupervised clustering on both MS1 and MS2 level to summarize all analytes of interest without assigning identities. This ensures that no valuable information is discarded due to analytes missing identification thresholds and as well allows us to spend more effort on the identification process due to the data reduction achieved by clustering.

Proteomics; Graphical Models; Clustering; Mass spectrometry; Data Analysis

**14/9 - Alex Fletcher (University of Sheffield): Mathematical modelling and analysis of epithelial morphogenesis**

Abstract: The study of morphogenesis - the generation of biological shape and form - promises to shed light on a wide range of developmental defects and inform strategies for the artificial growth of organs. Recently, the experimental study of morphogenesis has thrived due to a rise in quantitative methods. The resulting avalanche of data motivates us to design quantitative hypotheses through mathematical models, make quantitative experimental predictions, devise methods for quantitative data analysis, and design methods for quantitative inference using models and data. In this talk, I describe our recent work on the integrative analysis of morphogenesis in epithelia, one of the major tissue types in animals. Focusing on a widely used cell-based model of epithelia, the vertex model, I discuss to what extent quantitative model predictions may be influenced by parameter values and implementation details. Next, I illustrate how such models can be used to help gain mechanistic insights into, and generate quantitative predictions on, morphogenetic processes such as tissue size control and axis extension. I then outline a method for estimating mechanical parameters of vertex models from imaging data and quantifying the uncertainty associated with such estimates. Together, these contributions help enable the quantitative study of epithelia for a wide range of applications.

**27/9 - Jukka Corander (Department of Biostatistics, University of Oslo): Resolving the mysteries of bacterial evolution by ultra-fast ABC inference.**

Abstract: DNA in bacteria is known to be a subject to multiple evolutionary forces, including mutations, homologous recombination and horizontal transfer of genes. Such changes may be beneficial, deleterious or selectively neutral. Several models have been proposed to explain the variation we see in the genomes of bacteria across natural populations, including ecotype and neutral models. In particular simple neutral models have been shown to have a surprisingly good fit to population surveys. However, in the light of most recent functional data we present conclusive evidence that both neutral and ecotype models provide poor explanations for the strong correlations discovered between accessory genome loci across multiple populations of Streptococcus pneumoniae, a major human pathogen. We introduce a mechanistic model of frequency-dependent selection operating via accessory genes which is able to accurately predict the changes to the composition of the populations following introduction of a vaccination campaign. Unrelated recent large-scale genome data from an E. coli population suggests that the frequency-dependent selection may be a common mechanism regulating the evolution of bacterial populations of many species. These modeling advances have been in practice enable by ultra-fast ABC inference based on Bayesian optimization, which can be up to 4 orders of magnitude faster than sequential population Monte Carlo. The general potential of this inference method is now harnessed by the new open-source software initiative ELFI, which offers automated parallelization and a flexible platform for algorithm developers.

https://www.nature.com/articles/s41559-017-0337-x

https://www.biorxiv.org/content/early/2018/08/28/400374

http://jmlr.csail.mit.edu/papers/v17/15-017.html

http://jmlr.csail.mit.edu/papers/v19/17-374.html

https://www.biorxiv.org/content/early/2018/08/28/400374

http://jmlr.csail.mit.edu/papers/v17/15-017.html

http://jmlr.csail.mit.edu/papers/v19/17-374.html

**28/9 - Kenneth C. Millett (Department of Mathematics, University of California Santa Barbara): Knots and Links in Proteins**

Abstract: Some proteins contain important topological structures: knots, slipknots, and links as well as spatial graphs if one includes cysteine bonds. As a consequence, the geometrical and topological character of these spatial structures is of interest to mathematicians as well as molecular biologists, biochemists and biophysicists. We will describe characterizations of these spatial geometric and topological structures within proteins.

**4/10 - Marco Longfils: Single diffusing particles observed through a confocal microscope: an application of the doubly stochastic Poisson point process**

Abstract: Diffusing particles observed with a confocal laser scanning microscope give rise to a doubly stochastic Poisson point process. In particular, the photon detected by the microscope in one pixel follows a Poisson distribution with parameter that depends on the particle positions in space, which is modelled as a Poisson point process. Many techniques such as Fluorescence correlation spectroscopy, Raster image correlation spectroscopy and photon counting histograms have been developed to study molecular transport in cells and solution. All these techniques are based on the statistics of the photon detection process.

We show that the moments of the photon detection process can be computed in terms of physically relevant parameters such as the diffusion coefficient of the particles, their brightness and others. As a direct consequence, the statistical accuracy of the above mentioned techniques can be evaluated. Thus, we can relate the different experimental parameters that affects the photon detection process to the accuracy of each techniques, allowing us to optimally design an experiment.

**5/10 - Charlotte Hemelrijk (University of Groningen): Collective motion of flocks in relation to a predator**

Abstract: Many species of animals live in groups. This is supposed to protect them against predation. Yet when animals aggregate, they are easier to detect from a distance due to the larger mass of the group. Two evolutionary computational models of collective motion (including ours) show that grouping is advantageous for survival of prey only when the predator can be confused as to whom to attack. This confusion effect we also studied in an experimental design with human ‘predators’ when attacking starlings that flock in a computer simulation called StarDisplay. Humans appeared to become more confused whom to attack, the larger and denser flocks are.

Grouping animals also seem to protect themselves actively against attacks by displaying many patterns of collective escape in relation to the presence of predators, such as herd, ball, flash expansion, agitation wave. Using two computational models, we explain how some of them may arise. Asking when patterns of collective escape appear and whether they offer extra protection to groups of prey, we recorded them for flocks of starlings in Rome. It became clear that some are a direct reaction to an attack of the raptor, others already to its mere presence. Remarkably, in our empirical data the display of patterns of collective escape does not reduce the raptor’s catch success, leaving interesting questions concerning their emergence and asking for new methods of studying them.

**25/10 - Harri Lähdesmäki (Department of Computer Science at Aalto University School of Science): Non-parametric methods for learning continuous-time dynamical systems**

Abstract: Conventional differential equation models are parametric. However, for many complex/real-world systems it is practically impossible to determine parametric equations or interactions governing the underlying dynamics, rendering conventional models unpractical in many applications. To overcome this issue, we propose to use nonparametric models for differential equations by defining Gaussian process priors for the vector-field/drift and diffusion functions. We have developed statistical machine learning methods that can learn the underlying (arbitrary) ODE and SDE systems without prior knowledge. We formulate sensitivity equations for learning or use automatic differentiation with explicitly defined forward simulator for efficient model inference. Using simulated and real data, we demonstrate that our non-parametric methods can efficiently learn the underlying differential equation system, show the models' capabilities to infer unknown dynamics from sparse data, and to simulate the system forward into future. I will also highlight how our non-parametric models can learn stochastic differential equation transformations of inputs prior to a standard classification or regression function to implement state-of-the-art methods for continuous-time (infinitely) deep learning.

https://arxiv.org/abs/1803.04303

https://arxiv.org/abs/1807.05748

https://arxiv.org/abs/1810.04066

**1/11 - Petter Mostad (Chalmers): Error rates for unvalidated medical age assessment procedures**

Abstract: During 2014–2015, Sweden received asylum applications from more than 240,000 people of which more than 40,000 were termed unaccompanied minors. In a large number of cases, claims by asylum seekers of being below 18 years were not trusted by Swedish authorities. To handle the situation, the Swedish national board of forensic medicine (Rättsmedicinalverket, RMV) was assigned by the government to create a centralized system for medical age assessments.

RMV introduced a procedure including two biological age indicators; x-ray of the third molars and magnetic resonance imaging of the distal femoral epiphysis. In 2017, a total of 9617 males and 337 females were subjected to this procedure. No validation study for the procedure was however published, and the observed number of cases with different maturity combinations in teeth and femur were unexpected given the claims originally made by RMV. We present a general stochastic model enabling us to study which combinations of age indicator model parameters and age population profiles are consistent with the observed 2017 data for males. We find that, contrary to some RMV claims, maturity of the femur, as observed by RMV, appears on average well before maturity of teeth. According to our estimates, approximately 15% of the tested males were children. These children had an approximate 33% risk of being classified as adults. The corresponding risk for an adult to be misclassified as a child was approximately 7%.

We determine uncertainties and ranges of estimates under reasonable perturbations of the prior. https://rdcu.be/6PNI

**7/11 - Thomas Schön (Dept. of Information Technology, Uppsala University): Assembling stochastic quasi-Newton algorithms using Gaussian processes**

Abstract: In this talk I will focus on one of our recent developments where we show how the Gaussian process (GP) can be used to solve stochastic optimization problems. Our main motivation for studying these problems is that they arise when we are estimating unknown parameters in nonlinear state space models using sequential Monte Carlo (SMC). The very nature of this problem is such that we can only access the cost function (in this case the likelihood function) and its derivative via noisy observations, since there are no closed-form expressions available. Via SMC methods we can obtain unbiased estimates of the likelihood function. However, our development is fully general and hence applicable to any stochastic optimization problem. We start from the fact that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Inspired by this we can start assembling new stochastic quasi-Newton-type algorithms, applicable in situations where we only have access to noisy observations of the cost function and its derivatives. We will show how we can make use of the GP model to learn the Hessian allowing for efficient solution of these stochastic optimization problems. Additional motivation for studying the stochastic optimization problem stems from the fact that it arise in almost all large-scale supervised machine learning problems, not least in deep learning. I will very briefly mention some ongoing work where we have removed the GP representation and scale our ideas to much higher dimensions (both in terms of the size of the dataset and the number of unknown parameters).

**21/11 - Josef Wilzén: Physiological Gaussian Process Priors for the Hemodynamics in fMRI Analysis**

Abstract: Inference from fMRI data faces the challenge that the hemodynamic system, that relates the underlying neural activity to the observed BOLD fMRI signal, is not known. We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modelled nonparametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD time series, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in a flexible way. The prior mean function may be generated from a standard LTI system, based on a canonical hemodynamic response function, or a more elaborate physiological model such as the Balloon model. This gives us the nonparametric flexibility of the GP, but allows the posterior to fall back on the physiologically based prior when the data are weak. Results on simulated data show that even with an erroneous prior for the GP, the proposed model is still able to discriminate between active and non-active voxels in a satisfactory way. The proposed model is also applied to real fMRI data, where our Gaussian process model in several cases finds brain activity where a baseline model with fixed hemodynamics does not.

## 2017

**26/1, Sebastian Engelke, Ecole Polytechnique Fédérale de Lausanne: Robust bounds for multivariate extreme value distributions**

Abstract: Univariate extreme value theory is used to estimate the value at risk of an asset in regions where few or no observations are available. It is based on the asymptotic result that the maximum of the data follows approximately a generalized extreme value distribution. Blanchet and Murthy (2016, http://arxiv.org/abs/1601.06858) recently studied worst case bounds for high exceedance probabilities that are robust against incorrect model assumptions of the extremal types theorem. For two or more dependent assets, multivariate extreme value theory provides an asymptotically justified framework for the estimation of joint exceedances. Here, the strength of dependence is crucial and it is typically modelled by a parametric family of distributions. In this work we analyse bounds that are robust against misspecification of the true dependence between assets. They arise as the explicit solution to a convex optimization problem and take a surprisingly simple form. In a financial context, these robust bounds can be interpreted as the worst-case scenarios of a systematic stress test. We show the importance of this approach in simulations and apply it to real data from finance. This is joint work with Jevgenijs Ivanovs (Aarhus University).

**2/2, Igor Rychlik: Spatio-temporal model for wind speed variability in Atlantic Ocean**

Abstract: Investments in wind energy harvesting facilities are often high. At the same time uncertainties for the corresponding energy gains are large. Therefore a reliable model to describe the variability of wind speed is needed to estimate the expected available wind power and return values, e.g. 100 years wind speeds expected length of the wind conditions favourable for the wind-energy harvesting and other statistics of interest.

In Northern Atlantic wind speeds can be successfully modelled by means of a spatio-temporal transformed Gaussian field. Its dependence structure is localized by introduction of time and space dependent parameters in the field. However rarely occurring hurricanes in Caribbean region are missed by the model. A new model is presented that will cover both Northern Atlantic and the Caribbean region where hurricanes occur.

The model has the advantage of having a relatively small number of parameters. These parameters have natural physical interpretation and are statistically fitted to represent variability of observed wind speed in ERA Interim reanalysis data set.

Some validations and applications of the model will be presented. Rice’s method is employed to estimate the 100 years wind speed in some spatial region. This talk presents an ongoing research.

In Northern Atlantic wind speeds can be successfully modelled by means of a spatio-temporal transformed Gaussian field. Its dependence structure is localized by introduction of time and space dependent parameters in the field. However rarely occurring hurricanes in Caribbean region are missed by the model. A new model is presented that will cover both Northern Atlantic and the Caribbean region where hurricanes occur.

The model has the advantage of having a relatively small number of parameters. These parameters have natural physical interpretation and are statistically fitted to represent variability of observed wind speed in ERA Interim reanalysis data set.

Some validations and applications of the model will be presented. Rice’s method is employed to estimate the 100 years wind speed in some spatial region. This talk presents an ongoing research.

**16/2, Måns Magnusson, Linköping University: Sparse Partially Collapsed MCMC for Parallel Inference in Topic Models**

Abstract: Topic models are widely used for probabilistic modelling of text. MCMC sampling from the posterior distribution is typically performed using a collapsed Gibbs sampler. We propose a parallel sparse partially collapsed Gibbs sampler and compare its speed and efficiency to state-of-the-art samplers for topic models. The experiments, which are performed on well-known small and large corpora, show that the expected increase in statistical inefficiency from only partial collapsing is smaller than commonly assumed. This minor inefficiency can be more than compensated by the speed-up from parallelization of larger corpora. The proposed algorithm is fast, efficient, exact, and can be used in more modelling situations than the ordinary collapsed sampler. Work to speed up the computations further using the Polya-Urn distribution will also be presented.

**2/3, Henrike Häbel, Final seminar / Slutseminarium: Pairwise interaction in 3D – the interplay between repulsive and attractive forces**

The spatial statistical analysis of the structure in materials is crucial for understanding and controlling their properties and function. For example, the transport of body fluids in hygiene products or the release of a drug from an oral formulation highly depends on the structure of the respective material. The material structure can be characterized in terms of its homogeneity and isotropy. In turn, characterization and modelling of the structure may provide valuable knowledge for ensuring high quality products and treatments. We study the pairwise interaction between points in three dimensions, which may be particle positions in a gel or locations of pore branching points in a porous pharmaceutical coating. The basis for our approach is a pairwise interaction Gibbs point process, which can be defined in terms of a pair-potential function describing the pairwise interaction. In this talk, I will present how different pair-potential functions relate to different material properties. I will present and contrast estimation methods while comparing spatial pairwise interactions to physical chemical attractive and repulsive forces. With this work, we want to contribute to the cross-disciplinary research on the characterization and modeling of materials with a rather simple and efficient methodology that can be applicable to various materials.

This seminar will be given as a final seminar of my Ph.D. studies including a discussion led by Mats Rudemo.

**9/3, Ottmar Cronie, The second-order analysis of marked spatio-temporal point processes: applications to earthquake data**

Abstract: A marked spatio-temporal point process (MSTPP) is a random element used to describe the spatial evolution of a set of incidents over time, when there is also some event-specific piece of information present. Typical applications involve earthquakes, where the marks are the associated magnitudes, and disease occurrences, where the marks may be some classification such as sex or age.

This talk introduces so-called marked second-order reduced moment measures, and thereby also K-functions, for (inhomogeneous) MSTPPs, in order to analyse and explicitly quantify dependence between points of different mark-categories in a MSTPP. These summary statistics are defined in a general form, so their definitions depend on the specific choices made for the mark-space and the mark-reference measure. We propose unbiased estimators as well as a new way of testing whether the marks are independent of their space-time locations.

By employing Voronoi intensity estimators to estimate the underlying intensity function, these new statistics are finally employed to analyse the well-known Andaman sea earthquake dataset. We confirm that clustering takes place between main and fore-/after-shocks at virtually all space and time scales. In addition, we find support for the idea that, conditionally on the space-time locations of the earthquakes, the magnitudes do not behave like an iid sequence.

**16/3,**

**Krzysztof Bartoszek, Uppsala University**

**, A punctuated stochastic model of adaptation**

Abstract: Contemporary stochastic evolution models commonly assume gradual change for a phenotype. However the fossil record and biological theory suggests that development is rather undergoing punctuated change. In this setup one assumes that there are very short time intervals during which dramatic change occurs and between these the species are at stasis. Motivated by this I will present a branching Ornstein-Uhlenbeck model with jumps at speciation points. I will in particular discuss a very recent result concerning weak convergence: for a classical central limit theorem to hold dramatic change has to be a rare event.

**23/3, Artem Kaznatcheev, University of Oxford: The evolutionary games that cancers play and how to measure them**

Abstract: Tumours are complex ecosystems with various cancerous and non-cancerous sub- populations of cells adopting a heterogeneous set of survival and propagation strategies. Evolutionary game theory (EGT) is a tool to make sense of such systems in both a theoretical and experimental setting. I will start with a minimal theoretical model that spatializes the 2-strategy pairwise Go-vs-Grow game and show that the edge effect of a static boundary (such as a blood vessel, organ capsule or basement membrane) allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. Then I will consider a slightly more complicated theoretical study of a 3-strategy game that couples a public and club good to model the social dilemmas of tumour acidity and vasculature and allows us to explore treatment order and timing. But this raises the question: how do we know if the interactions are a Go-vs-Grow game or double goods game? In general, we guess these games from intuitions acquired by looking at population level experiments. This looking can be formalized into an operational specification of an effective game. I will show how we measure such an effective game in ALK+ non-small cell lung cancer, and that – like in the theoretical study of the double goods game -- the presence or absence of treatment changes the qualitative type of game (and not just its quantitative details). However, this effective game collapses the local interactions -- reductive game -- and spatial structure into a single measurement. This is in contrast to a typical study of space in EGT -- like the spatialized Go-vs-Grow game -- that starts with the reductive game and then simulate that interaction over a graph (or other model of space) to show a surprising difference in dynamics between the spatial model and the inviscid mean-field. Hence, I advocate that we turn the typical space-in-EGT study on its head. Let’s start from the measurement of an effective game and an operationalization of spatial structure to then provide a method for inferring the reductive game. I will sketch some ideas on how to approach this through time-lapse microscopy of the Petri dish.

**30/3, Robert Noble, ETH Basel: Evolution, ecology, and cancer risk: from naked mole rats to modern humans**

Abstract:Mathematical models of cancer initiation conventionally examine how rapidly a cell population acquires a certain number of mutational “hits” or “drivers”. However, to understand variation in cancer risk, we must consider two additional factors. First, ecology: just as the fate of a normal stem cell depends on its niche, the relative fitness of a transformed cell depends on its microenvironment. Second, organismal evolution: tissues that generate more mutations are at greater risk of invasive neoplasms and thus are expected to have evolved more effective cancer prevention mechanisms, such as tissue compartmentalization. Extrinsic factors (such as tobacco smoke, UV radiation, diet, and infections) can alter cancer risk by changing the microenvironment, as well as by influencing stem cell division rates or mutation rates. I will present a reanalysis of recently published data that reveals a major effect of anatomical location on cancer risk, compelling us to reframe the question of how much cancer is due to unavoidable “bad luck”. I will argue that most modern-day cancer is in fact due to environments deviating from central tendencies of distributions that have prevailed during cancer resistance evolution. Otherwise, cancer risk across the tree of life almost never exceeds ~5%. I will support this claim with case-study demographic models for humans and naked mole rats (until recently thought to be virtually immune to cancer). The overarching framework provides a basis for understanding how cancer risk is shaped by evolution and environmental change.

**6/4, John Wiedenhoeft, Rutgers University: Fast Bayesian Inference of Copy Number Variants using Hidden Markov Models with Wavelet Compression**

Hidden Markov Models (HMM) play a central role in the statistical analysis of sequential data. For reasons of computational efficiency, classic frequentist methods such as Baum-Welch and Viterbi decoding are still widely used, despite drawbacks including locally maximal likelihood estimates. While recent advances in computing power have increasingly enabled the use of Bayesian methods, they are not able to cope with sequences comprising multiple millions or billions of observations as they arise for example in whole genome sequencing. We show that wavelet theory can be used to derive a simple dynamic data compression scheme to drastically improve speed and convergence behaviour of Forward-Backward Gibbs sampling in HMM, allowing for Bayesian inference of the marginal distributions of several million latent state variables in a matter of seconds to a few minutes.

**18/5, Lloyd Demetrius, Harvard University, Max Planck Institut: An entropic selection principle in evolutionary processes**

The Entropic Selection Principle states that the outcome of competition between related populations of metabolic entities – macromolecules, cells, higher organisms – is contingent on the resource constraints, and determined by

*evolutionary entropy*, a statistical measure of the diversity of pathways of energy flow between these interacting elements.I will describe the mathematical basis for the selection principle, and then discuss its application to

(i) the evolution of life history

(ii) the origins and evolution of cooperation

(iii) the origin and propagation of age-related diseases.

(i) the evolution of life history

(ii) the origins and evolution of cooperation

(iii) the origin and propagation of age-related diseases.

Ref: Boltzmann, Darwin and Directionality Theory,

*Physics Reports*, vol. 530 (2013)**1/6, Daniel Nichol, The Institute of Cancer Research: Collateral Sensitivity is Contingent on the Repeatability of Evolution**

Abstract: The emergence of drug resistance is governed by Darwinian evolution. Therapeutic strategies that account for these evolutionary principles are needed to maintain the efficacy of antibiotics or to overcome resistance to cancer therapies. One such strategy is the identification of drug sequences wherein the evolution of resistance to each drug sensitises the population to the next; a phenomenon known as collateral sensitivity. Recently, experimental evolution has been used to find such sequences. I present mathematical modelling, coupled with experimental validation, indicating that drug strategies designed through experimental evolution often suggest collateral sensitivity where cross resistance ultimately occurs. This divergence in clinical response occurs as evolutionary trajectories are not necessarily repeatable in rugged fitness landscapes and low-replicate-number experiments can miss divergent trajectories. Using empirically derived estimates for these fitness landscapes, I demonstrate the potential for model-driven-design of drug sequences that minimise the likelihood of highly resistant disease arising. Finally, I explore the challenges of designing experimental studies to predict evolution and suggest an alternative approach that combines mathematical modelling, experimental evolution and distributed collection of clinical data.

**8/6, Jie Yen Fan, Monash University:**

**Limit theorems for size, age, type, and type structure dependent populations**

We consider a multi-type population model in which individual lifespan and reproduction depend on the population size and composition, over ages and types of individuals. Under the assumption that the initial population is large and the dependence upon demographical conditions smooth, we give the Law of Large Numbers and Central Limit Theorem for the population density, i.e. the population size and composition over ages and types normed by its habitat carrying capacity, as the latter tends to infinity. The Law of Large Numbers, in its turn, yields a multi-dimensional generalised McKendrick-von Foerster differential equation, and the Central Limit Theorem shows that the limit process satisfies a new stochastic partial differential equation. The key to the analysis is Sobolev embedding. An important case is populations with two types, females and males, where only females reproduce, but with a fertility, influenced by the availability of males. Thus, modelling of mating (which is often not evident and even irrelevant, like in fish and algae) can be bypassed in the study of populations with sexual reproduction.

**12/10, Aila Särkkä: Anisotropy analysis of spatial point patterns**

Abstract: In the early spatial point process literature, observed point patterns were typically small and no repetitions were available. It was natural to assume that the patterns were realizations of stationary and isotropic point processes. Nowadays, large data sets with repetitions have become more and more common and it is important to think about the validity of these assumptions. Non-stationarity has gotten quite a lot of attention during the recent years and it is straightforward to include it in many point process models. Isotropy, on the other hand, is often still assumed without further checking, and even though there are several tools suggested to detect isotropy and test for it, they have not been so widely used.

This seminar will give an overview of nonparametric methods for anisotropy analysis of (stationary) point processes. Methods based on nearest neighbour and second order summary statistics as well as spectral and wavelet analysis will be discussed. The techniques will be illustrated on both a clustered and a regular example. Finally, one of the methods will be used to estimate the deformation history in polar ice using the measured anisotropy of air inclusions from deep ice cores.

This seminar will give an overview of nonparametric methods for anisotropy analysis of (stationary) point processes. Methods based on nearest neighbour and second order summary statistics as well as spectral and wavelet analysis will be discussed. The techniques will be illustrated on both a clustered and a regular example. Finally, one of the methods will be used to estimate the deformation history in polar ice using the measured anisotropy of air inclusions from deep ice cores.

**14/12, David Bolin: The SPDE approach for Gaussian random fields with general smoothness**Abstract: A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form Lβu = W, where W is Gaussian white noise, L is a second-order differential operator, and β > 0 is a parameter that determines the smoothness of u. However, this approach has been limited to the case 2β ∈ N, which excludes several important covariance models such as the exponential covariance on R2.

We demonstrate how this restriction can be avoided by combining a finite element discretization in space with a rational approximation of the function x−β to approximate the solution u. For the resulting approximation, an explicit rate of strong convergence is derived and we show that the method has the same computational benefits as in the restricted case 2β ∈ N when used for statistical inference and prediction. Several numerical experiments are performed to illustrate the accuracy of the method, and to show how it can be used for likelihood-based inference for all model parameters including β.

## 2016

**21/1, Håvard Rue, NTNU: Penalising model component complexity: A principled practical**

**approach to constructing priors**

Abstract: Setting prior distributions on model parameters is the act of characterising the nature of our uncertainty and has proven a critical issue in applied Bayesian statistics. Although the prior distribution should ideally encode the users' uncertainty about the parameters, this level of knowledge transfer seems to be unattainable in practice and applied statisticians are forced to search for a ``default'' prior. Despite the development of objective priors, which are only available explicitly for a small number of highly restricted model classes, the applied statistician has few practical guidelines to follow when choosing the priors. An easy way out of this dilemma is to re-use prior choices of others, with an appropriate reference.

In this talk, I will introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys' priors, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations, like random effect models, spline smoothing, disease mapping, Cox proportional hazard models with time-varying frailty, spatial Gaussian fields and multivariate probit models. Further, we show how to control the overall variance arising from many model components in hierarchical models.

**26/1, Stephen Senn, Luxembourg Institute of Health:**

**P-values: The Problem is not What You Think**

Abstract: There is a modern folk-history of statistical inference that goes like this. Following the work of Bayes and Laplace, scientists had been treading a path of inferential virtue for a century and a half. Along came RA Fisher and seduced them to folly. Chief among the sins he corrupted them to indulge in were significance tests and P-values. These encourage scientists to ‘find’ effects more easily than they should. This, combined with the earthly success that positive results can bring, has caused scientists to become addicted to a dangerous inferential drug that is poisoning science. Now, thanks to the power of computing, the omens are good that they can be weaned from their addiction and brought back onto the path of inferential virtue.

I claim, however, that the history is false. P-values did not develop as an alternative to Bayesian significance tests which, in any case, are themselves an inferential device which many who claim to be Bayesian do not use, but as an alternative interpretation of a standard Bayesian result in common use. A key, but rather neglected, figure in 20th century statistics is CD Broad who pointed to a severe problem with the Bayes-Laplace application of inverse probability: reasonable support, let alone proof, of the truth of a scientific law cannot be obtained from standard priors. The Bayesian significance test was developed by Harold Jeffreys in response to Broad’s analysis but, at least in medical statistics, it has remained a little-used approach to practical Bayesian inference.

The real issue is not one of conflict between P-values and Bayesian inference but one between two different forms of Bayes. This conflict is sharp but eradicating P-values will do nothing to resolve it.

**28/1, Ola Izyumtseva, Kiev State University: Self-intersection local time of Gaussian processes. New approach**

Abstract: The talk is devoted to the local times and self-intersection local times for Gaussian processes. Local times in one dimension and self-intersection local times in two dimension are important geometric characteristics related to large number of process properties. The well-known example which illustrates such relationship is Le Gall asymptotic expansion for the area of Wiener sausage containing renormalized self-intersection local times. In contrast to local times of one dimensional process self-intersection local times of two dimensional process for proper definition require renormalization. Up to recently, such a renormalization was constructed by S. Varadhan, E.B. Dynkin, J. Rosen only for a Wiener process. The mentioned results essentially relay on Markov property, self-similarity and other nice properties of Wiener process. We introduce a new approach based on investigation of geometry of a Hilbert-valued function generating the Gaussian process and apply it to establish existence of local times and renormalized self-intersection local times. Our approach is applicable to a wide class of Gaussian non-Markov processes. The application of self-intersection local times for the modelling of random polymers will also be discussed. (In collaboration with A.A. Dorogovtsev).

**2/2,**

**Erik-Jan Wagenmakers, University of Amsterdam**

**, A Predictive Perspective on Bayesian Inference**

Abstract: In mathematical psychology, Bayesian model selection is often used to adjudicate between competing accounts of cognition and behaviour. One of the attractions of Bayesian model selection is that it embodies an automatic Occam's razor – a reward for parsimony that is the result of an averaging process over the prior distribution.

Here I provide a predictive interpretation of Bayes inference, encompassing not only Bayesian model selection, but also Bayesian parameter estimation. This predictive interpretation supports a range of insights about the fundamental properties of learning and rational updating of knowledge.

Here I provide a predictive interpretation of Bayes inference, encompassing not only Bayesian model selection, but also Bayesian parameter estimation. This predictive interpretation supports a range of insights about the fundamental properties of learning and rational updating of knowledge.

**25/2, Marcin Lis, Planar Ising model as a gas of cycles**

Abstract: I will talk about a new representation of the planar Ising model in terms of a Poisson point process of cycles in the graph. This is a direct analog of the continuous result of Werner which represents the Conformal Loop Ensemble (a random collection of continuous simple curves) via a Poisson point process of Brownian loops in the plane. Surprisingly, the new correspondence on the discrete level is valid for all values of the temperature parameter (unlike the continuum one, which only holds at criticality). I will discuss implications of this fact and outline possible applications to solve some of the remaining open questions about the Ising model.

**3/3, Krzysztof Podgorski, Lund University, Event based statistics for dynamical random fields**

Abstract: The sea surface is a classical example of stochastic field that is evolving in time.

Extreme events that are occurring on such a surface are random and of interest for practitioners - ocean engineers are interested in large waves and damage they may cause to an oil platform or to a ship. Thus data on the ocean surface elevation are constantly collected by system of buoys, ship- or air-borne devices, and satellites all around the globe. These vast data require statistical analysis to answer important questions about random events of interest. For example, one can ask about statistical distribution of wave sizes, in particular, how distributed large waves are or how steep they are. Waves often travel in groups and a group of waves typically causes more damage to a structure or a ship than an individual wave even if the latter is bigger than each one in the group. So one can be interested in how many waves there is per group or how fast groups are travelling in comparison to individual waves.

Extreme events that are occurring on such a surface are random and of interest for practitioners - ocean engineers are interested in large waves and damage they may cause to an oil platform or to a ship. Thus data on the ocean surface elevation are constantly collected by system of buoys, ship- or air-borne devices, and satellites all around the globe. These vast data require statistical analysis to answer important questions about random events of interest. For example, one can ask about statistical distribution of wave sizes, in particular, how distributed large waves are or how steep they are. Waves often travel in groups and a group of waves typically causes more damage to a structure or a ship than an individual wave even if the latter is bigger than each one in the group. So one can be interested in how many waves there is per group or how fast groups are travelling in comparison to individual waves.

In the talk, a methodology that analyse statistical distributions at random events defined on random process is presented. It is based on a classical result of Rice and allows for computation of statistical distributions of events sampled from the sea surface.

The methodology initially was applied to Gaussian models but in fact, it is also valid for quite general dynamically evolving stochastic surfaces. In particular, it is discussed how sampling distributions for non-Gaussian processes can be obtained through

Slepian models that describe the distributional form of a stochastic process observed at level crossings of a random process. This is used for efficient simulations of the behaviour of a random processes sampled at crossings of a non-Gaussian moving average process. It is observed that the behaviour of the process at high level crossings is fundamentally different from that in the Gaussian case, which is in line with some recent theoretical results on the subject.

The methodology initially was applied to Gaussian models but in fact, it is also valid for quite general dynamically evolving stochastic surfaces. In particular, it is discussed how sampling distributions for non-Gaussian processes can be obtained through

Slepian models that describe the distributional form of a stochastic process observed at level crossings of a random process. This is used for efficient simulations of the behaviour of a random processes sampled at crossings of a non-Gaussian moving average process. It is observed that the behaviour of the process at high level crossings is fundamentally different from that in the Gaussian case, which is in line with some recent theoretical results on the subject.

**10/3,**

**Bengt Johannesson, Volvo, Design Strategies of Test Codes for Durability Requirement of Disk Brakes in Truck Application**

Abstract: Durability requirements for disk brakes in truck application are improved based on the actual customer usage. A second moment reliability index is used to design test codes for the assessment of variable amplitude disk brake fatigue life. The approach is based on the mean estimates of logarithms of equivalent strength of the brake and customer load variables. The index gives possibilities to take all uncertainties in the fatigue life assessment into account, including scatter in material, production, and usage but also systematic errors like model errors in test set up, stress calculations, damage hypothesis, as well as statistical uncertainties.

**22/3, Hermann Thorisson, University of Iceland, Palm Theory and Shift-Coupling**

Abstract: Palm versions w.r.t. stationary random measures are mass-stationary, that is, the origin is at a typical location in the mass of the random measure. For a simple example, consider the stationary Poisson process on the line conditioned on having a point at the origin. The origin is then at a typical point (at a typical location in the mass) because shifting the origin to the n:th point on the right (or on the left) does not alter the fact that the inter-point distances are i.i.d. exponential. Another (less obvious) example is the local time at zero of a two-sided standard Brownian motion.

In this talk we shall first consider mass-stationarity on the line and the shift-coupling problem of how to shift the origin from a typical location in the mass of one random measure to a typical location in the mass of another random measure. We shall then extend the view beyond the line, moving through the Poisson process in the plane and d-dimensional space towards general random measures on groups.

**14/4, Omiros Papaspiliopoulos, Universitat Pompeu Fabra, stochastic processes for learning and uncertainty quantification**

Abstract: in the talk I will focus on the use of stochastic processes for building algorithms for probing high-dimensional distributions as appear in statistical learning problems, in particular Bayesian learning, and for uncertainty quantification. More specifically, I will give an accessible overview of how stochastic differential equations are used to build Markov chain Monte Carlo algorithms and will then move on to some current work I am involved with that combines these ideas with auxiliary variables in order to obtain a good tradeoff between mixing

and computational efficiency.

and computational efficiency.

**21/4, Alexandre Antonelli, Professor in Systematics and Biodiversity, Dept of Biological and Environmental Sciences, University of Gothenburg: Hundreds of millions of DNA sequences and species observations: Challenges for synthesizing biological knowledge**

The loss of biodiversity is one of the most serious threats to society, yet we still lack a basic understanding of how many species there are, where they occur, how they evolved, and how they may be affected by global warming and land use. In this talk I will present some of the major prospects and challenges faced by biologists in the 21st century, focusing on the methodological tools that our group is developing to make sense out of rapidly increasing data volumes. I will focus on i) building the Tree of Life that unites all living organisms and their timing of origination, ii) mapping the distribution of all life on Earth, and iii) understanding how the world’s various ecosystems originated and responded to changes in the landscape and climate. Biodiversity research is now entering a new and exciting phase, where mathematical and statistical sciences hold the potential to make a huge contribution by increased collaboration and innovative solutions.

**28/4, Peter J Diggle, CHICAS, Lancaster Medical School, Lancaster University: Model-Based Geostatistics for Prevalence Mapping in Low-Resource Settings**

Abstract: In low-resource settings, prevalence mapping relies on empirical prevalence data from a finite, often spatially sparse, set of surveys of communities within the region of interest, possibly supplemented by remotely sensed images that can act as proxies for environmental risk factors. A standard geostatistical model for data of this kind is a generalized linear mixed model with logistic link, binomial error distribution and a Gaussian spatial process as a stochastic component of the linear predictor.

In this talk, I will first review statistical methods and software associated with this standard model, then consider several methodological extensions whose development has been motivated by the requirements of specific applications including river-blindness mapping Africa-wide.

Diggle, P.J. and Giorgi, E. (2016). Model-based geostatistics for prevalence Mapping in

low-resource settings (with Discussion). Journal of the American Statistical Association

(to appear).

low-resource settings (with Discussion). Journal of the American Statistical Association

(to appear).

**12/5, Ute Hahn, Aarhus University: Monte Carlo envelope tests for high dimensional data or curves**

Abstract: Monte Carlo envelopes compare an observed curve with simulated counterparts to test the hypothesis that the observation is drawn from the same distribution as the simulated curves. The simulated curves are used to construct an acceptance band, the envelope. If the observed curve leaves the envelope, the test rejects the hypothesis. These methods are popular, for example,to test goodness of fit for spatial point processes, where the information contained in point patterns is boiled down to a summary function. The summary function is estimated on both the observation and on simulated realizations of the null model. However, the usual practice to draw an acceptance band from pointwise empirical quantiles bears an inherent multiple testing problem, and yields liberal tests in most cases.

This talk introduces a graphical envelope test that has proper size. We will also see how the test principle can be extended to group wise comparison by permutation, or to high dimensional data that are not represented as curves, such as images. Based on joint work with Mari Myllymäki (Natural Resources Institute Finland), Tomáš Mrkvička (University of South Bohemia) and Pavel Grabarnik (Laboratory of Ecosystems Modeling, the Russian Academy of Sciences).

**26/5, Martin Foster, University of York: A Bayesian decision-theoretic model of sequential experimentation with delayed response**

Abstract: We propose a Bayesian decision-theoretic model of a fully sequential experiment in which the real-valued primary end point is observed with delay. The goal is to identify the sequential experiment which maximises the expected benefits of a technology adoption decision, minus sampling costs. The solution yields a unified policy defining the optimal `do not experiment'/`fixed sample size experiment'/`sequential experiment' regions and optimal stopping boundaries for sequential sampling, as a function of the prior mean benefit and the size of the delay. We apply the model to the field of medical statistics, using data from published clinical trials.

**1/9, Fima Klebaner, Monash University: On the use of Sobolev spaces in limit theorems for the age of population**

Abstract: We consider a family of general branching processes with reproduction parameters depending on the age of the individual as well as the population age structure and a parameter K, which may represent the carrying capacity. These processes are Markovian in the age structure. We give the Law of Large Numbers of a measure-valued process, and the Central Limit Theorem as a distribution-valued process. While LLN recovers known PDE, the CLT yields new SPDE.

This is joint work with Peter Jagers (Chalmers), Jie Yen Fan and Kais Hamza (Monash)

**15/9, Joseba Dalmau, Université Paris-Sud: The distribution of the quasispecies**

In 1971, Manfred Eigen proposed a deterministic model in order to describe the evolution of an infinite population of macromolecules subject to mutation and selection forces. As a consequence of the study of Eigen’s model, two important phenomena arise: the error threshold and the quasispecies. In order to obtain a counterpart of this results for a finite population, we study a Moran model with mutation and selection, and we recover, in a certain asymptotic regime, the error threshold and the quasispecies phenomena. Furthermore, we obtain an explicit formula for the distribution of the quasispecies.

**22/9, Sophie Hautphenne, EPFL: A pathwise iterative approach to the extinction of branching processes with countably many types**

Abstract: We consider the extinction events of Galton-Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton-Watson processes with finite but increasing sets of types. A pathwise approach is then used to show that, under some sufficient conditions, the corresponding sequence of extinction probability vectors converges to the global extinction probability vector of the Galton-Watson processes with countably infinitely many types. Besides giving rise to a number of novel iterative methods for computing the global extinction probability vector, our approach paves the way to new global extinction criteria for branching processes with countably infinitely many types.

**29/9, Umberto Picchini, Lund University: A likelihood-free version of the stochastic approximation EM algorithm (SAEM) for inference in complex models**

Abstract: We present an approximate maximum likelihood methodology for the parameters of incomplete data models. A likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm is constructed to maximize the likelihood function of model parameters. While SAEM is best suited for models having a tractable "complete likelihood" function, its application to moderately complex models is difficult, and results impossible for models having so-called intractable likelihoods. The latter are typically treated using approximate Bayesian computation (ABC) algorithms or synthetic likelihoods, where information from the data is carried by a set of summary statistics. While ABC is considered the state-of-art methodology for intractable likelihoods, its algorithms are often difficult to tune. On the other hand, synthetic likelihoods (SL) is a more recent methodology which is less general than ABC, it requires stronger assumptions but also less tuning. By exploiting the Gaussian assumption set by SL on data summaries, we can construct a likelihood-free version of SAEM. Our method is completely plug-and-play and available for both static and dynamic models, the ability to simulate realizations from the model being the only requirement. We present simulation studies from our on-going work: preliminary results are encouraging and are compared with state-of-art methods for maximum likelihood inference (iterated filtering), Bayesian inference (particle marginal methods) and ABC.

**6/10, Jakob Björnberg: Random loop models on trees**

Abstract: Certain models in statistical physics may be studied via ensembles of random loops. Of particular interest is the question whether infinite loops occur or not, since this is of relevance to phase transition in the physics model. One may consider such models defined on various graphs, and in this talk we focus on regular trees of large degree. We sketch the main ideas of joint work together with D. Ueltschi in which we estimate the critical point for the occurrence of infinite loops.

**20/10, Georg Lindgren, Lund University: Stochastic properties of optical black holes**

Abstract: "Light can be twisted like a corkscrew around its axis of travel. Because of the twisting, the light waves at the axis itself cancel each other out. When projected onto a flat surface, an optical vortex looks like a ring of light, with a dark hole in the center. This corkscrew of light, with darkness at the center, is called an optical vortex." Wikipedia

The statistical properties near phase singularities in a complex wavefield is described as the conditional distributions of the real and imaginary Gaussian components, given a common zero crossing point. The exact distribution is expressed as a Slepian model, where a regression term provides the main structure, with parameters given by the gradients of the Gaussian components at the singularity, and Gaussian non-stationary residuals that provide

local variability. This technique differs from the linearization (Taylor expansion) technique commonly used.

The empirically and theoretically verified elliptic eccentricity of the intensity contours in the vortex core is a property of the regression term, but with different normalization compared to the classical theory. The residual term models the statistical variability around these ellipses. The radii of the circular contours of the current magnitude are similarly modified by the new regression expansion and also here the random deviations are modelled by the residual field.

The statistical properties near phase singularities in a complex wavefield is described as the conditional distributions of the real and imaginary Gaussian components, given a common zero crossing point. The exact distribution is expressed as a Slepian model, where a regression term provides the main structure, with parameters given by the gradients of the Gaussian components at the singularity, and Gaussian non-stationary residuals that provide

local variability. This technique differs from the linearization (Taylor expansion) technique commonly used.

The empirically and theoretically verified elliptic eccentricity of the intensity contours in the vortex core is a property of the regression term, but with different normalization compared to the classical theory. The residual term models the statistical variability around these ellipses. The radii of the circular contours of the current magnitude are similarly modified by the new regression expansion and also here the random deviations are modelled by the residual field.

**27/10, Daniel Ahlberg, IMPA and Uppsala University: Random coalescing geodesics in first-passage percolation**

Abstract: A random metric on \mathbb{Z}^2 is obtained by assigning non-negative i.i.d. weights to the edges of the nearest neighbour lattice. We shall discuss properties of geodesics in this metric. We develop an ergodic theory for infinite geodesics via the study of what we shall call `random coalescing geodesics’. Random coalescing geodesics have a range of nice properties. By showing that they are (in some sense) dense is the space of geodesics, we may extrapolate these properties to all infinite geodesics. As an application of this theory we answer a question posed by Benjamini, Kalai and Schramm in 2003, that has come to be known as the `midpoint problem’. This is joint work with Chris Hoffman.

**3/11, KaYin Leung, Stockholm University, Dangerous connections: the spread of infectious diseases on dynamic networks**

In this talk we formulate models for the spread of infection on dynamic networks that are amenable to analysis in the large population limit. We distinguish three different levels: (1) binding sites, (2) individuals, and (3) the population. In the tradition of physiologically structured population models, the model formulation starts at the individual level. Influences from the `outside world’ on an individual are captured by environmental variables which are population-level quantities. A key characteristic of the network models is that individuals can be decomposed into a number of (conditionally) independent components: each individual has a fixed number of `binding sites’ for partners. Moreover, individual-level probabilities are obtained from binding-site-level probabilities by combinatorics while population level quantities are obtained by averaging over individuals with respect to age. The Markov chain dynamics of binding sites are described by only a few equations. Yet we are able to characterize population-level epidemiological quantities such as R_0, which is a threshold parameter for the stability of the trivial steady state of the population-level system. In this talk we show how probabilistic arguments can be used to derive an explicit R_0 for an, in principle, large dimensional system of ODE.

This talk is based on joint work with Odo Diekmann and Mirjam Kretzschmar (Utrecht, The Netherlands)

This talk is based on joint work with Odo Diekmann and Mirjam Kretzschmar (Utrecht, The Netherlands)

**24/11, Yi He, Tilburg University: Asymptotics for Extreme Depth-based Quantile Region Estimation**

Abstract: A data depth function provides a probability based ordering from the center (the point with maximal depth value) outwards. Consider the small-probability quantile region in arbitrary dimensions consisting of extremely outlying points with nearly zero data depth value. Since its estimation involves extrapolation outside the data cloud, an entirely nonparametric method often fails. Using extreme value statistics, we extend the semiparametric estimation procedures proposed in Cai, Einmahl and de Haan (AoS,2011) and He and Einmahl (JRSSb,2016) to incorporate various depth functions. Under weak regular variation conditions, a general consistency result is derived. To construct confidence sets that asymptotically cover the extreme quantile region or/and its complement with a pre-specified probability, we introduce new notions of distance between our estimated and true quantile region and prove their asymptotic normality via an approximation using the extreme value index only. Refined asymptotics are derived particularly for the half-space depth to include the shape estimation uncertainty. The finite-sample coverage probabilities of our asymptotic confidence sets are evaluated in a simulation study for the half-space depth and the projection depth.

**1/12, Marianne Månsson: Statistical methodology and challenges in the area of prostate cancer screening**

To screen or not to screen for prostate cancer in a population-based manner has been an ongoing discussion for decades in Sweden and many other countries. No country has found it justifiable to introduce a general screening program so far. Meanwhile so-called opportunistic screening has become more and more common. At the Department of Urology at Sahlgrenska two randomized screening studies are on-going: The first one started 1994 and is in its end phase (~20000 men), while the new one started in 2015 (~40-60000 men). With these studies as a starting point, statistical methodology and challenges in this kind of studies will be discussed. In particular the issue of overdiagnosis will be considered.

**8/12, Holger Rootzén: Human life is unbounded -- but short**

The longest-living known person, Jeanne Calment, died August 4, 1997 at the age of 122 years and 164 days. Is there a sharp upper limit for the length of human life, close to this age? A Nature letter (doi:10.1038/nature19793) a month and a half ago claimed this is the case. We did not find the arguments compelling and have hence used extreme value statistics to try to understand what the two existing databases on supercentenarians, humans who have lived 110 years or more, really say. Results include that there is no difference in survival between women and men after 110 years, but that around 10 times as many women as men survive to 110; that data from western countries seems homogeneous, but that Japanese data is different; that there is little evidence of a time trend (though this is less clear); and that the overall picture is that human life is unbounded -- but short: the yearly survival rate after 110 is about 50%/year. As one consequence it is not unlikely that during the next 20 years, and at the present stage of medicine and technology, someone (probably a woman) will live to be 120, but quite unlikely that anyone will live more than 130 years. Of course, dramatic progress in medicine might change this picture completely. The results come from ongoing and preliminary work, and we very much hope for input from the audience to help improving our understanding. This is joint work with Dmitrii Zholud.

**15/12, Martin Schlather, University of Mannheim, Simulation of Max-Stable Random Fields**

Abstract: The simulation algorithm for max-stable random fields I had suggested in 2002 has several drawbacks. Among others, it is inexact and it is slow for larger areas. One improvement is an efficient simulation algorithm that relies on theoretical results of the choice of the spectral representation (Oesting, Schlather, Zhou, submitted). Another improvement is on the computational side, especially for large areas, by generalising an algorithm of D\"oge (2001) on the simulation of a model in stochastic geometry, the random sequential absorption model. The latter is work in progress.

## 2015

**29/1, Trifon Missov, Max Planck Institute for Demography, Stochastic Models in Mortality Research: Recent Advancements and Applications**

Abstract: Stochastic models in mortality research aim to capture observed mortality dynamics over multiple time dimensions (ages, periods, and cohorts), on the one hand, and relate longevity to biological processes, on the other hand. Frailty models provide the basic mathematical tool for studying mortality curves and surfaces. This talk focuses on recent developments in fixed-frailty and changing-frailty (dynamic-frailty) models reflecting observed mortality phenomena: the mortality plateau, the persistent decline in age-specific mortality rates ("lifesaving"), etc.

**12/1, Sergei Zuyev, Optimal sampling of stochastic processes via measure optimisation technique**

Abstract. Let W(t) be a continuous non-stationary stochastic process on [0,1] which can be observed at times T=(t_0 < t_1 < ... t_n) giving rise to a random vector W=(W(t_1),...,W(t_n)). The question we address is how to choose the sampling times T in such a way that the linear spline constructed through the points (T,W) deviates as little as possible from the trajectory (W(t), t in [0,1])? Namely, the average L_2 distance between the paths is minimised. The answer depends on the smoothness coefficient a(t), meaning that the average increment E|W(t+s)-W(t)| behaves like |s|^a(t) for small s. The local variant of the problem for a monotone a(t) was addressed previously by Hashorva, Lifshits and Seleznjev. By using the variation technique on measures we are able to extend the known results and potentially to attack multi-dimensional case of optimal sampling of random fields.

**19/2, Alexey Lindo and Serik Sagitov, A special family of Galton-Watson processes with explosions**

Abstract: The linear-fractional Galton-Watson processes is a well known case when many characteristics of a branching process can be computed explicitly. In this paper we extend the two-parameter linear-fractional family to a much richer four-parameter family of reproduction laws. The corresponding Galton-Watson processes also allow for explicit calculations, now with possibility for infinite mean, or even infinite number of offspring. We study the properties of this special family of branching processes, and show, in particular, that in some explosive cases the time to explosion can be approximated by the Gumbel distribution.

**26/2,**

**Jean-Baptiste Gouéré, Université d'Orléans**

**, Continuum percolation on R^d**

Abstract:

We consider the Boolean model on R^d. This is the union of i.i.d. random Euclidean balls centered at points of an homogeneous Poisson point process on R^d. Choose the intensity of the Poisson point process so that the Boolean model is critical for percolation. In other words, if we lower the intensity then all the connected components of the Boolean model are bounded, while if we increase the intensity then there exists one unbounded component. We are interested in the volumetric proportion of R^d which is covered by this critical Boolean model. This critical volumetric proportion is a function of the dimension d and of the common distribution of the radii. We aim to study this function.

**12/3, Daniel Simpson, Norwegian University of Science and Technology: With low power comes great responsibility: challenges in modern spatial data analysis**

Abstract:

Like other fields in statistics, spatial data analysis has undergone its own "big data" revolution. Over the last decade, this has resulted in new approximate algorithms and new approximate models being used to fit ever more complicated data. There is a particular role in this revolution for model-based statistics and, in particular, Bayesian analysis.

The trouble is that as both the data and the models expand, we can end up with complex, unidentifiable, hierarchical, unobserved nightmares. Hence we are starting to seriously ask the question "What can we responsibly say about this data?".

In this talk, I will go nowhere near answering this fundamental question, but I will provide a clutch of partial answers to simpler problems. In particular, I will outline the trade-offs that need to be considered when building approximate spatial models; the incorporation of weak expert knowledge into priors on the hyper-parameters of spatial models; the dangers of flexible non-stationarity; and the role of prior choice in interpreting posteriors.

This is joint work with Geir-Arne Fuglstad, Sigrunn Sørbye, Janine Illian, Finn Lindgren, and Håvard Rue.

**19/3,**

**Emmanuel Schertzer, Sorbonne, France**

**, The contour process of Crump-Mode-Jagers trees**

Abstract: The genealogy of a (planar) Galton-Watson branching process is encoded by its contour path, which is obtained by recording the height of an exploration particle running along the edges of the tree from left to right.

Crump-Mode-Jagers (CMJ) branching processes are a generalization of Galton-Watson trees, for which generations can overlap. In general, the contour process of such trees is difficult to characterize. However, we will show that under certain assumptions, it is obtained by a simple transformation of the contour process of the underlying genealogical structure. This work sheds some new light on previous results obtained by Sagitov on the large time behaviour of CMJ branching processes. This is joint work with Florian Simatos.

**23/4,**

**David Dereudre, Université Lille-1, Consistency of likelihood estimation for Gibbs point processes**

Abstract: We prove the strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models. The setting is very general and includes pairwise pair potentials, finite and infinite multibody interactions and geometrical interactions, where the range can be finite or infinite. Moreover the Gibbs interaction may depend linearly or non-linearly on the parameters, a particular case being hardcore parameters and interaction range parameters. As important examples, we deduce the consistency of the MLE for all parameters of the Strauss model, the hardcore Strauss model, the Lennard-Jones model and the area-interaction model.

**7/5, Olle Häggström, The current debate on p-values and null hypothesis significance testing**

Abstract: The use of p-values and null hypothesis significance testing has been under attack in recent years from practitioners of statistics in various disciplines. One highlight is the publication in 2008 of "The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives" by Stephen Ziliak and Deirdre McCloskey. Another is the ban of p-values from the journal Basic and Applied Social Psychology that its editors announced in February 2015. I will review (parts of) this debate, and stress how important I think it is that we, as statisticians, take part in it.

**21/5, Jürgen Potthoff, University of Mannheim, Sample Properties of Random Fields**

Abstract: A rather general version of the celebrated

*Kolmogorov–Chentsov*–theorem is presented, which provides sufficient criteria for the existence of a (Hölder) continuous modification of a random field, which is indexed by a metric space admitting certain separability properties. For random fields on an open subset of the*d*–dimensional euclidean space sufficient criteria are presented which guarantee the existence of a sample differentiable modification. If time permits, results concerning the existence of separable and/or measurable modifications are mentioned.**28/5, Ingemar Kaj, Uppsala universitet, The Poisson random field site frequency spectrum**

Abstract: We study a class of Poisson random measures with intensity measure given by the law of the Wright-Fisher diffusion process, which arises as a limiting model for genetic divergence between species. Each species is a population of gene sequences subject to mutational change under neutral or selective evolution. Using the duality relation between Wright-Fisher diffusions and Kingman's coalescent process we derive the non-equilibrium site frequency spectrum. Applications include certain genomic measures used to assess sequence divergence during speciation (such as F_{ST} and dN/dS).

**11/6, Fima Klebaner, Monash University, Limit theorems for age distribution in populations with high carrying capacity**

Abstract: We prove fluid and central limit approximations for measure valued ages under smooth demographic assumptions.

Joint work with Fan, Hamza (Monash) and Jagers (Chalmers).

Joint work with Fan, Hamza (Monash) and Jagers (Chalmers).

**23/6, Carmen Minuesa, University of Extremadura, Robust estimation for Controlled Branching Processes**

Abstract: Controlled branching processes are appropriate probabilistic models for the description of population dynamics in which the number of individuals with reproductive capacity in each generation is controlled by a random mechanism. The probabilistic theory of these processes has been extensively developed, being an important issue to examine the inferential problems arising from them.

The aim of this work is to consider the estimation of the underlying offspring parameters via disparities, assuming that the offspring distribution belongs to a general parametric family.

From a frequentist viewpoint, we obtain the minimum disparity estimators under three possible samples: given the entire family tree up to a certain generation, given the total number of individuals and progenitors in each generation, and given only the population sizes and we examine their asymptotic and robustness properties.

From a Bayesian outlook, we develop an analogous procedure which provides robust Bayesian estimators of the offspring parameter through the use of disparities. The method consists of replacing the log likelihood with an appropriately scaled disparity in the expression of the posterior distribution. For the estimators associated to the resulting distribution, we study their asymptotic properties.

Finally, we illustrate the accuracy of the proposed methods by the way of simulated examples developed with the statistical software R.

The aim of this work is to consider the estimation of the underlying offspring parameters via disparities, assuming that the offspring distribution belongs to a general parametric family.

From a frequentist viewpoint, we obtain the minimum disparity estimators under three possible samples: given the entire family tree up to a certain generation, given the total number of individuals and progenitors in each generation, and given only the population sizes and we examine their asymptotic and robustness properties.

From a Bayesian outlook, we develop an analogous procedure which provides robust Bayesian estimators of the offspring parameter through the use of disparities. The method consists of replacing the log likelihood with an appropriately scaled disparity in the expression of the posterior distribution. For the estimators associated to the resulting distribution, we study their asymptotic properties.

Finally, we illustrate the accuracy of the proposed methods by the way of simulated examples developed with the statistical software R.

**8/9,**

**K. Borovkov, The University of Melbourne, On the asymptotic behaviour of a dynamic version of the Neyman contagious point process**

We consider a dynamic version of the Neyman contagious point process that can be used for modelling the spatial dynamics of biological populations, including species invasion scenarios. Starting with an arbitrary finite initial configuration of points in R^d with nonnegative weights, at each time step a point is chosen at random from the process according to the distribution with probabilities proportional to the points' weights. Then a finite random number of new points is added to the process, each displaced from the location of the chosen "mother" point by a random vector and assigned a random weight. Under broad conditions on the sequences of the numbers of newly added points, their weights and displacement vectors (which include a random environments setup), we derive the asymptotic behaviour of the locations of the points added to the process at time step n and also that of the scaled mean measure of the point process after time step n-->oo.

**24/9, Laurent Decreusefond, ENST, France, Distances between point processes**

Abstract: Point processes can be mathematically viewed both as a set of points or as a combination of Dirac measures. Depending on the point of view, the distance between two realizations of some point processes can be naturally defined of different manners. This induces different distances between distributions of random point processes. We show on several examples how these distances can be defined and estimated.

**1/10, Tailen Hsing, Analysing Spatial Data Locally**

Abstract: Stationarity is a common assumption in spatial statistics. The justification is often that stationarity is a reasonable approximation if data are collected "locally." In this talk we first review various known approaches for modeling nonstationary spatial data. We then examine the notion of local stationarity in more detail. In particular, we will consider a nonstationary model whose covariance behaves like the Matern covariance locally and an inference approach for that model based on gridded data.

**8/10, Evsey Morozov, Inst. Applied Math. Research, Russia, Stability analysis of regenerative queues: some recent results**

Abstract: We consider a general approach to stability (positive recurrence) of the regenerative queueing systems, which is based on an asymptotic property of the embedded renewal process of regenerations. The renewal process obeys a useful characterization of the limiting remaining regeneration time allowing, for a wide class of queues, to establish minimal stability conditions by the following two-step procedure. At the first step, a negative drift condition is used to prove that the basic process does not go to infinity in probability. Then, at the second step, using a regeneration condition, we show that, starting within a compact set, the process regenerates in a finite time with a positive probability. It implies the finiteness of the mean regeneration period (positive recurrence). This approach is effective beyond the class of Markovian models.

To illustrate the approach, we present some recent results related, in particular, to retrial systems, state-dependent systems, cascade systems.

**15/10, Johan Lindström, Lund University: Seasonally Non-stationary Smoothing Splines: Post-processing of Satellite data**

Abstract: Post-processing of satellite remote sensing data is often done to reduce noise and remove artefacts due to atmospheric (and other) disturbances. Here we focus specifically on satellite derived vegetation indices which are used for large scale monitoring of vegetation cover, plant health, and plant phenology. These indices often exhibit strong seasonal patterns, where rapid changes during spring and fall contrast to relatively stable behaviour during the summer and winter season. The goal of the post-processing is to extract smooth seasonal curves that describe how the vegetation varies during the year. This is however complicated by missing data and observations with large biases.

Here a method for post-processing of satellite based time-series is presented. The method combines seasonally non-stationary smoothing spline with observational errors that are modelled using a normal-variance mixture. The seasonal non-stationarity allows us to capture the different behaviour during the year, and the error structure accounts for the biased and heavy tailed errors induced by atmospheric disturbances. The model is formulated using Gaussian Markov processes and fitted using MCMC.

**20/10,**

**Janine B Illian,**

**University of St Andrews and NTNU Trondheim**

**:**

**Spatial point processes in the modern world – an interdisciplinary dialogue**

Abstract: In the past, complex statistical methods beyond those covered in standard statistics textbooks would be developed as well as applied by a statistician. Nowadays, freely available, sophisticated software packages such as R are in common use and at the same time increasing amounts of data are collected. As a result, users have both, a stronger need for analysing these data themselves as well as an increasing awareness of the existence of the advanced methodology since it is no longer “hidden” from them in inaccessible statistical journals. As a result, statisticians make their methodology usable

In this talk, we argue that is necessary to make methods usable and for this to be successful there needs to be a strong interaction with the user community through interdisciplinary work. This implies not only making model fitting feasible by developing computationally efficient methodology to reduce running times but also to improve the practicality of other aspects of the statistical analysis such as model construction, prior choice and interpretation as these equally relevant for users with real data sets and real scientific questions. We discuss the importance of an intense interdisciplinary dialogue for statistics to become relevant in the real world by illustrating it through discussing past and current examples of this ongoing dialogue in the context of spatial point processes and their application – mainly in the context of ecological research.

**2**

**2/10, Sach Mukherjee, German Center for Neurodegenerative Diseases (DZNE): High-dimensional statistics for personalized medicine**

Abstract: Human diseases show considerable heterogeneity at the molecular level. Such heterogeneity is central to personalized medicine efforts that seek to exploit molecular data to better understand disease biology and inform clinical decision making. An emerging notion is that diseases and disease subgroups may differ with respect to patterns of molecular interplay. I will discuss our ongoing efforts to develop statistical methods to investigate such heterogeneity with an emphasis on high-dimensional and causal aspects.

29/10: Peter Olofsson, Trinity University: A stochastic model of speciation through Bateson-Dobzhansky-Muller incompatibilitiesAbstract: Speciation is characterized by the development of reproductive isolating barriers between diverging groups. Intrinsic post-zygotic barriers of the type envisioned by Bateson, Dobzhansky, and Muller are deleterious interactions among loci that reduce hybrid fitness, leading to reproductive isolation. The first stochastic model of the development of these barriers was published by Orr in 1995. We generalize Orr's model by incorporating finite protein–protein interaction networks and by allowing for different fixation rates at different loci. Formulas for the speciation probability and the expected time until speciation are established.
5/11, Murray Pollock, University of Warwick: A New Unbiased and Scalable Monte Carlo Method for Bayesian InferenceAbstract: This talk will introduce novel methodology for exploring posterior distributions by modifying methodology for exactly (without error) simulating diffusion sample paths – the Scalable Langevin Exact Algorithm (ScaLE). This new method has remarkably good scalability properties (among other interesting properties) as the size of the data set increases (it has sub-linear cost, and potentially no cost), and therefore is a natural candidate for “Big Data” inference.
Joint work with Paul Fearnhead (Lancaster), Adam Johansen (Warwick) and Gareth Roberts (Warwick).12/11, Jimmy Olsson, KTH, Efficient particle-based online smoothing in general state-space hidden Markov models: the PaRIS algorithmAbstract: This talk discusses a novel algorithm, the particle-based, rapid incremental smoother (PaRIS), for efficient online approximation of smoothed expectations of additive state functionals in general hidden Markov models. The algorithm, which has a linear computational complexity under weak assumptions and very limited memory requirements, is furnished with a number of convergence results, including a central limit theorem. An interesting feature of PaRIS, which samples on-the-fly from the retrospective dynamics induced by the particle filter, is that it requires two or more backward draws per particle in order to cope with degeneracy of the sampled trajectories and to stay numerically stable in the long run with an asymptotic variance that grows only linearly with time. |

19/1

19/1

**1, Patri**k Albin:**On Extreme Value Theory for Group Stationary Gaussian**

**Processes**

Abstract: We study extreme value theory of right stationary Gaussian processes with parameters in open subsets with compact closure of (not necessarily Abelian) locally compact topological groups. Even when specialized to Euclidian space our result extend results on extremes of stationary Gaussian processes and fields in the literature by means of requiring weaker technical conditions as well as by means of the fact that group stationary processes need not be stationary in the usual sense (that is, with respect to addition as group operation).

**26/11, Youri K. Belyaev, Umeå University, The Hybrid Moments-Distance method for clustering observations with a mixture of two symmetrical distributions**

Joint work with D. Källberg and P. Rydén

Abstract:

Clustering cancer patients based on high-dimensional gene expression data are essential in discovering new subtypes of cancer. Here we present a novel univariate clustering approach that can be used for variable selection in high-dimensional clustering problems.

We observe gene expression data on one gene and n patients, where the jth patient has cancer of type 1 (tj =1) or type 2 (tj =2). The aim is to predict the unobservable list of types {t1,...,tn}.

Here {t1,...,tn} are values of i.i.d. random variables {T1,...,Tn} such that P[Tj =1]=w1, P[Tj =2]=w2 and w1+ w2=1. The gene expression data {x1,…,xn} are observations of i.i.d. random variables {X1,…,Xn}, where Xj has distribution F1 if tj=1 and F2 if tj=2, j=1,…,n. We assume that F1 and F2 are symmetrical distributions parameterized by their means (m1 and m2) and variances (v1 and v2). Thereby we have a statistical model with mixture of two symmetrical distributions with five unknown parameters {w1, m1, v1, m2, v2}. Consistent estimates of all 5 parameters can be found by using the recursive EM-algorithm and the responsibilities {q1(x1),…,qn(xn)} obtained via the estimated parameters can be used to predict the patients’ cancer types {t1,...,tn}. However, the EM-algorithm is sensitive to distribution assumptions that deviates from the real distributions F1, F2 and on the starting point in the recursion.

We propose an alternative method, the hybrid moment-distance (HMD) method, where the observations {x1,…,xn} are used for estimation of the first three moments. These moment estimates are used to reduce the dimensional space of parameters from 5 to 3. The optimal parameters within the lower space are obtained by considering the distance between the empirical distribution and the fitted parametric distributions. Responsibilities {q1(x1),…,qn(xn)}, obtained via the HMD-method’s estimated parameters, are used to predict the patients’ cancer types. Note that the patient´s q-value is the estimated probability that the patient has cancer of certain type.

An extensive simulation study showed that the HMD-algorithm outperformed the EM-algorithm with respect to clustering their performance. The HMD-method was flexible and performed well also under very imprecise model assumptions, which suggest that it is robust and well suited for real problems.

Abstract:

Clustering cancer patients based on high-dimensional gene expression data are essential in discovering new subtypes of cancer. Here we present a novel univariate clustering approach that can be used for variable selection in high-dimensional clustering problems.

We observe gene expression data on one gene and n patients, where the jth patient has cancer of type 1 (tj =1) or type 2 (tj =2). The aim is to predict the unobservable list of types {t1,...,tn}.

Here {t1,...,tn} are values of i.i.d. random variables {T1,...,Tn} such that P[Tj =1]=w1, P[Tj =2]=w2 and w1+ w2=1. The gene expression data {x1,…,xn} are observations of i.i.d. random variables {X1,…,Xn}, where Xj has distribution F1 if tj=1 and F2 if tj=2, j=1,…,n. We assume that F1 and F2 are symmetrical distributions parameterized by their means (m1 and m2) and variances (v1 and v2). Thereby we have a statistical model with mixture of two symmetrical distributions with five unknown parameters {w1, m1, v1, m2, v2}. Consistent estimates of all 5 parameters can be found by using the recursive EM-algorithm and the responsibilities {q1(x1),…,qn(xn)} obtained via the estimated parameters can be used to predict the patients’ cancer types {t1,...,tn}. However, the EM-algorithm is sensitive to distribution assumptions that deviates from the real distributions F1, F2 and on the starting point in the recursion.

We propose an alternative method, the hybrid moment-distance (HMD) method, where the observations {x1,…,xn} are used for estimation of the first three moments. These moment estimates are used to reduce the dimensional space of parameters from 5 to 3. The optimal parameters within the lower space are obtained by considering the distance between the empirical distribution and the fitted parametric distributions. Responsibilities {q1(x1),…,qn(xn)}, obtained via the HMD-method’s estimated parameters, are used to predict the patients’ cancer types. Note that the patient´s q-value is the estimated probability that the patient has cancer of certain type.

An extensive simulation study showed that the HMD-algorithm outperformed the EM-algorithm with respect to clustering their performance. The HMD-method was flexible and performed well also under very imprecise model assumptions, which suggest that it is robust and well suited for real problems.

**10/12:**

**Anna-Kaisa Ylitalo, University of Jyväskylä**

**:**

**Eye movements during music reading - A generalized estimating equation approach**

Abstract: Eye tracking has long research traditions in text reading and picture inspection, but studies on eye movements in music reading are still relatively rare. Thus there is no standardised methodology for analysing eye movements in music reading and, in fact, rather little is known about visual processing of musical notation at all. In our experiment participants read and performed simple melodies on an electric piano. Some of the melodies included melodic skips and we study how these skips affect visual processing of the melody. In addition, we are interested in the effects of tempo, participant’s expertise and placement of melodic skips. The eye movement data are analysed using generalised estimating equation (GEE) approach, which is an extension of generalised linear models (GMLs) to longitudinal data.

## 2014

**30/1, Andrea Ghiglietti, Milan University**

**: A two-colour Randomly Reinforced Urn design targeting fixed allocations**

Abstract:

There are many experimental designs for clinical trials, in which the proportion of patients allocated to treatments converges to a fixed value. Some of these procedures are response-adaptive and the limiting allocation proportion can depend on treatment behaviours. This property makes these designs very attractive because they are able to achieve two simultaneous goals: (a) collecting evidence to determine the superior treatment, and (b) increasing the allocation of units to the superior treatment. We focus on a particular class of adaptive designs, described in terms of urn models which are randomly reinforced and characterized by a diagonal mean replacement matrix, called Randomly Reinforced Urn (RRU) designs. They usually present a probability to allocate units to the best treatment that converges to one as the sample size increases. Hence, many asymptotic desirable properties concerning designs that target a proportion in (0,1) are not straightforwardly fulfilled by these procedures. Then, we construct a modified RRU model which is able to target any asymptotic allocations in (0,1) fixed in advance. We prove the almost sure convergence of the urn proportion and of the proportion of colours sampled by the urn. We are able to compute the exact rate of convergence of the urn proportion and to characterize the limiting distribution. We also focus on the inferential aspects concerning this urn design. We consider different statistical tests, based either on adaptive estimators of the unknown means or on the urn proportion. Suitable statistics are introduced and studied to test the hypothesis on treatment difference.

There are many experimental designs for clinical trials, in which the proportion of patients allocated to treatments converges to a fixed value. Some of these procedures are response-adaptive and the limiting allocation proportion can depend on treatment behaviours. This property makes these designs very attractive because they are able to achieve two simultaneous goals: (a) collecting evidence to determine the superior treatment, and (b) increasing the allocation of units to the superior treatment. We focus on a particular class of adaptive designs, described in terms of urn models which are randomly reinforced and characterized by a diagonal mean replacement matrix, called Randomly Reinforced Urn (RRU) designs. They usually present a probability to allocate units to the best treatment that converges to one as the sample size increases. Hence, many asymptotic desirable properties concerning designs that target a proportion in (0,1) are not straightforwardly fulfilled by these procedures. Then, we construct a modified RRU model which is able to target any asymptotic allocations in (0,1) fixed in advance. We prove the almost sure convergence of the urn proportion and of the proportion of colours sampled by the urn. We are able to compute the exact rate of convergence of the urn proportion and to characterize the limiting distribution. We also focus on the inferential aspects concerning this urn design. We consider different statistical tests, based either on adaptive estimators of the unknown means or on the urn proportion. Suitable statistics are introduced and studied to test the hypothesis on treatment difference.

**6/2, David Bolin, Chalmers: Multivariate latent Gaussian random field mixture models**

Abstract: A novel class of models is introduced, with potential areas of application ranging from land-use classification to brain imaging and geostatistics. The model class, denoted latent Gaussian random filed mixture models, combines the Markov random field mixture model with latent Gaussian random field models. The latent model, which is observed under measurement noise, is defined as a mixture of several, possible multivariate, Gaussian random fields. Which of the fields that is observed at each location is modelled using a discrete Markov random field. In order to use the model class for massive data sets that arises in many possible areas of application, such as brain imaging, a computationally efficient parameter estimation method is required. Such an estimation method, based on a stochastic gradient algorithm, is developed and the model is tested on a magnetic resonance imaging application.

**13/2, Ege Rubak, Aalborg University, Denmark: Determinantal point processes - statistical modeling and inference**

Determinantal point process (DPP) models constitute one of the few non-Poisson point process model classes where we have access to closed form expressions for both the likelihood function and the moments. Furthermore, we have an exact simulation algorithm which avoids the use of Markov chain Monte Carlo methods. In this talk I will define a DPP and briefly review some of these appealing properties which make DPP models well suited for statistical analysis. I will then demonstrate how simulation and statistical inference for DPPs is carried out in practice using software developed in R. Specifically, I will show how we have analysed several real datasets using this software and the DPP framework. This includes model specification, parameter estimation, simulation from the fitted model, and goodness-of-fit assessment.

Time permitting, I will end the talk with a brief demonstration of how recent developments allow us to extend the software to handle stationary DPPs on a sphere (e.g. the surface of Earth).

The main part of the work has been carried out in collaboration with Jesper Möller from Aalborg University and Frederic Lavancier from Nantes University, while the final part concerning DPPs on spheres is an ongoing collaboration which also includes Morten Nielsen (Aalborg University).

Time permitting, I will end the talk with a brief demonstration of how recent developments allow us to extend the software to handle stationary DPPs on a sphere (e.g. the surface of Earth).

The main part of the work has been carried out in collaboration with Jesper Möller from Aalborg University and Frederic Lavancier from Nantes University, while the final part concerning DPPs on spheres is an ongoing collaboration which also includes Morten Nielsen (Aalborg University).

**20/2, Anthony Metcalfe, KTH, Universality classes of lozenge tilings of a polyhedron**

Joint work with Kurt Johansson and Erik Duse.

Abstract: A regular hexagon can be tiled with lozenges of three different orientations. Letting the hexagon have sides of length n, and the lozenges have sides of length 1, we can consider the asymptotic behaviour of a typical tiling as n increases. Typically, near the corners of the hexagon there are regions of "frozen" tiles, and there is a "disordered" region in the centre which is approximately circular.

More generally one can consider lozenge tilings of polyhedra with more complex boundary conditions. In this talk we use steepest descent analysis to examine the local asymptotic behaviour of tiles in various regions. Tiles near the boundary of the equivalent "frozen" and "disordered" regions are of particular interest, and we give necessary conditions under which such tiles behave asymptotically like a determinantal random point field with the Airy kernel. We also classify necessary conditions that lead to other asymptotic behaviours, and examine the global asymptotic behaviour of the system by considering the geometric implications of these conditions.

Abstract: A regular hexagon can be tiled with lozenges of three different orientations. Letting the hexagon have sides of length n, and the lozenges have sides of length 1, we can consider the asymptotic behaviour of a typical tiling as n increases. Typically, near the corners of the hexagon there are regions of "frozen" tiles, and there is a "disordered" region in the centre which is approximately circular.

More generally one can consider lozenge tilings of polyhedra with more complex boundary conditions. In this talk we use steepest descent analysis to examine the local asymptotic behaviour of tiles in various regions. Tiles near the boundary of the equivalent "frozen" and "disordered" regions are of particular interest, and we give necessary conditions under which such tiles behave asymptotically like a determinantal random point field with the Airy kernel. We also classify necessary conditions that lead to other asymptotic behaviours, and examine the global asymptotic behaviour of the system by considering the geometric implications of these conditions.

**27/2, Sergei Zuyev, Chalmers: Discussion seminar: Probing harmony with algebra (or attractiveness with statistics)**

Abstract: In a recent statistical study, US researches quantified attractiveness of a face by using measures of deviation from canonical "standards" like equality of eye width to interocular distance or golden ratio of nose to chin distance to nose width. The actual attractiveness formula is kept as a commercial secret, but using available published data we shall discuss if attractiveness is really a function of the geometry of a face and to which extent the harmony can be described by the algebra (even statistically)

**6/3, Tuomas Rajala, Chalmers: Denoising polar ice data using point pattern statistics**

Abstract: Point pattern statistics analyses point configurations suspended in 2- and 3 dimensional volumes of continuous material or space. An example is given by the bubble patterns within polar ice samples, drilled from the ice sheets of Antarctica and Greenland in order to study the climate conditions of the past. The problem with the ice data is that the original configuration of bubbles is overlaid with artefacts that appear during the extraction, transit and storage of the physical samples. This talk will discuss the problem together with some ideas for removing the artefacts.

**13/3, Pierre Nyqvist, KTH: Importance sampling through a min-max representation for viscosity solutions to Hamilton-Jacobi equations**

Abstract:

In applied probability, a lot of effort has been put into the design of efficient simulation algorithm for problems where the standard Monte Carlo algorithm, for various reasons, becomes too inefficient for practical purposes. This happens particularly in the rare-event setting, in which poor precision and/or a high computational cost renders the algorithm virtually useless. As a remedy, different techniques for variance reduction have been developed, such as importance sampling, interacting particle systems and multi-level splitting, MCMC techniques etc.

The focus of this talk will be importance sampling. One way to design efficient algorithms, first discovered by Dupuis and Wang, is the so-called subsolution approach: the sampling algorithm is based on a subsolution to a (problem-specific) Hamilton-Jacobi equation. The aim of the talk will be two-fold: First, to discuss the connections between importance sampling, large deviations and Hamilton-Jacobi equations. Second, to present a recent result of ours that concerns viscosity solutions to Hamilton-Jacobi equations and which enables the construction of efficient algorithms. Given time, the method will be illustrated with an example in the small diffusion setting (the Freidlin-Wentzell theory of large deviations).

The talk is based on joint work with Henrik Hult and Boualem Djehiche. It is as much an overview of the subsolution approach as a presentation of our results. In particular, it will encompass the talk that Professor Djehiche gave in November as well as discuss the relevant background.

**20/3, Arvind Singh, Orsay: Localization of a vertex-reinforced random walk on Z**

Abstract:

We consider the model of the vertex-reinforced random walk on the integer Lattice. Roughly speaking, it is a process which moves, at each unit of time, toward a neighbouring vertex with a probability proportional to a function of the time already spent at that site. When the reinforcement function is linear, Pemantle and Volkov showed that the walk visits only finitely many sites. This result was subsequently improved by Tarrès who showed that the walk get stuck on exactly 5 sites almost surely. In this talk, we discuss the case of sub-linear and super-linear reinforcement weights and show that a wide range of localization patterns may occur.

**8/4, Aernout van Enter, Groningen, The Netherlands: Bootstrap percolation, the role of anisotropy: Questions, some answers and applications**

Abstract:

Bootstrap percolation models describe growth processes, in which in a metastable situation nucleation occurs from the creation of some kind of critical droplet.

Such droplets are rare, but once they appear, they grow to cover the whole of space. The occurrence of such critical droplets in large volumes is ruled by asymptotic probabilities. We discuss how the scaling of these probabilities with the volume is modified in the presence of anisotropy. Moreover we discuss why numerics have

rather bad track record in the subject. This is based on joint work with Tim Hulshof, Hugo Duminil-Copin, Rob Morris and Anne Fey.

**10/4,**

**Rasmus Waagepetersen, Department of Mathematical Sciences, Aalborg University: Quasi-likelihood for spatial point processes**

Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates. When Cox or cluster process models are used to accommodate clustering not accounted for by the available covariates, likelihood based inference becomes computationally cumbersome due to the complicated nature of the likelihood function and the associated score function. It is therefore of interest to consider alternative more easily computable estimating functions. We derive the optimal estimating function in a class of first-order estimating functions. The optimal estimating function depends on the solution of a certain Fredholm integral

equation which in practise is solved numerically. The derivation of the optimal estimating function has close similarities to the derivation of quasi-likelihood for standard data sets. The approximate solution is further equivalent to a quasi-likelihood score for binary spatial data. We therefore use the term quasi-likelihood for our optimal estimating function approach. We demonstrate in a simulation study and a data example that our quasi-likelihood method for spatial point processes is both statistically and computationally efficient.

**24/4, Oleg Seleznjev, Umeå University: Linear approximation of random processes with variable smoothness**

Abstract:

We consider the problem of approximation of a locally stationary random process with a variable smoothness index defined on an interval. An example of such function is a multifractional Brownian motion, which is an extension of the fractional Brownian motion with path regularity varying in time. Probabilistic models based on the locally stationary random processes with variable smoothness became recently an object of interest for applications in various areas (e.g., Internet traffic, financial records, natural landscapes) due to their flexibility for matching local regularity properties, e.g., [3]. Approximation of continuous and smooth random functions with unique singularity point is studied in [1].

We consider the problem of approximation of a locally stationary random process with a variable smoothness index defined on an interval. An example of such function is a multifractional Brownian motion, which is an extension of the fractional Brownian motion with path regularity varying in time. Probabilistic models based on the locally stationary random processes with variable smoothness became recently an object of interest for applications in various areas (e.g., Internet traffic, financial records, natural landscapes) due to their flexibility for matching local regularity properties, e.g., [3]. Approximation of continuous and smooth random functions with unique singularity point is studied in [1].

Assuming that the smoothness index attains its unique minimum in the interval (an isolated singularity point), we propose a method for construction of observation points sets (sampling designs) in approximation (piecewise constant approximation, [2], and splines). For such methods, we find the exact asymptotic rate for the integrated mean square error. Further, we show that the suggested rate is optimal, e.g., convergence is faster than for conventional regular designs. The obtained results can be used in various problems in signal processing, e.g., in optimization of compressing digitized signals, in numerical analysis of random functions, e.g., in simulation studies with controlled accuracy for functionals on realizations of random processes.

Keywords: variable smoothness, multifractional Brownian motion, piecewise constant approximation,

Hermite splines.

Hermite splines.

References:

[1] Abramowicz, K. and Seleznjev, O. (2011). Spline approximation of a random process with singularity. J. Statist. Plann. Inference 141, 1333–1342.

[2] Hashorva, E., Lifshits, M., and Seleznjev, O. (2012). Approximation of a random process with variable smoothness. ArXiv:1206.1251v1.

[3] Echelard, A., Lévy Véhel, J., Barriére, O. (2010). Terrain modeling with multifractional Brownian motion and self-regulating processes. In: Computer Vision and Graphics. LNCS, 6374, Springer, Berlin, 342–351.

[1] Abramowicz, K. and Seleznjev, O. (2011). Spline approximation of a random process with singularity. J. Statist. Plann. Inference 141, 1333–1342.

[2] Hashorva, E., Lifshits, M., and Seleznjev, O. (2012). Approximation of a random process with variable smoothness. ArXiv:1206.1251v1.

[3] Echelard, A., Lévy Véhel, J., Barriére, O. (2010). Terrain modeling with multifractional Brownian motion and self-regulating processes. In: Computer Vision and Graphics. LNCS, 6374, Springer, Berlin, 342–351.

**20/5, Simo Särkkä, Dept. of Biomedical Engineering and Computational Science, Aalto University, Finland: > Theory and Practice of Particle Filtering for State Space Models**

The aim of this talk is to give an introduction to particle filtering, which refers to a powerful class of sequential Monte Carlo methods for Bayesian inference in state space models. Particle filters can be seen as approximate optimal (Bayesian) filtering methods which can be used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications and medicine. Smartphones have also created a recent demand for this kind of sophisticated sensor fusion and non-linear multichannel signal processing methods, as they provide a wide range of motion and environmental sensors together with the computational power to run the methods in real time. The aim of this talk is to provide an introduction to particle filtering in theoretical and algorithmic level as well as to outline the main results in analysis of convergence of particle filters.

**15/5, Marie-Colette van Lieshaut, CWI, The Netherlands: A Spectral Mean for Point Sampled Closed Curves**

Abstract:

We propose a spectral mean for closed curves described by sample points on its boundary subject to misalignment and noise. First, we ignore misalignment and derive maximum likelihood estimators of the model and noise parameters in the Fourier domain. We estimate the unknown curve by back-transformation and derive the distribution of the integrated squared error. Then, we model misalignment by means of a shifted parametric diffeomorphism and minimise a suitable objective function simultaneously over the unknown curve and the misalignment parameters. Finally, the method is illustrated on simulated data as well as on photographs of Lake Tana taken by astronauts during a Shuttle mission.

**27/5, Nanny Wermuth, Johannes Gutenberg-University, Mainz, Traceable regressions: general properties and some special cases**

Traceable regressions are those graphical Markov models that are best suited to capture generating processes in longitudinal studies, either without or with interventions. Sequences of responses may contain several component variables and these components may be continuous or discrete.

In this lecture, I discuss properties of corresponding distributions that are needed to read off the graph all implied independences, as well as the additional properties that permit similar conclusions about dependences. Some data analyses are shown and some results are discussed for star graphs, a very special type of graph.

In this lecture, I discuss properties of corresponding distributions that are needed to read off the graph all implied independences, as well as the additional properties that permit similar conclusions about dependences. Some data analyses are shown and some results are discussed for star graphs, a very special type of graph.

**12/6, F. C. Klebaner, Monas University, Melbourne: When is a Stochastic Exponential of a Martingale a true Martingale?**

Abstract:

The question "When is a Stochastic Exponential E(M) of a Martingale M a true Martingale?" is important in financial mathematics. The best known sufficient condition is due to Novikov, and another one due to Kazamaki. Here we give another condition, which is essentially a linear growth condition on the parameters of the original martingale M. These conditions generalize Benes' idea, but the proofs use a different approach. They are applicable when Novikov's or Kazamaki conditions do not apply. Our approach works for processes with jumps, as well as non-Markov processes. This is joint work with Robert Liptser.

**2/9, Pavel Grabarnik, Laboratory of Ecosystems Modeling, the Russian Academy of Sciences: Spatial complexity of ecosystems: testing models for spatial point patterns**

Abstract:

Goodness-of-fit tests play a fundamental role in ecological statistics and modeling. Testing statistical hypotheses is an important step in building models. Often it is checked whether the data deviate significantly from a null model. In spatial point pattern analysis, typical null models are complete spatial randomness, independent marking or some fitted model. Unlike in classical statistics, where null models are usually represented by a single hypothesis, the hypotheses in spatial statistics have a spatial dimension and therefore a multiple character.

The classical device to overcome the multiple comparison problem in testing a spatial hypothesis is the deviation test, which summarizing differences between an empirical test function and its expectation under the null hypothesis, which depend on a distance variable. Another test is based on simulation envelopes, where a data functional statistic is inspected for a range of distances simultaneously. It was noted that type I error probability, when testing over an interval of distances, exceeds that for individual scales heavily, and therefore, the conventional pointwise simulation envelope test cannot be recommended as a rigorous statistical tool.

To overcome this drawback the refined envelope test was proposed in (Grabarnik et al., 2011) and developed further in a recent work (Myllymaki et al.,2013). It is a procedure where the global type I error probability is evaluated by simulation and taken into account in making conclusions. In this way, it becomes a valuable tool both for statistical inference and for understanding the reasons of possible rejections of the tested hypothesis.

A problem related to testing a goodness-of-fit of fitted models is that the test may be extremely conservative. The remedy is the procedure proposed by Dao and Genton (2013). Based on their idea we suggest a way how to adjust envelopes to make the empirical type I error equal to the nominal one.

We illustrate the applicability of the tests by examples from forest ecology.

References.

Dao, N. A., & Genton, M. G. (2013). A Monte Carlo adjusted goodness-of-fit test for parametric models describing spatial point patterns. Journal of Computational and Graphical Statistics, 23, 497-517.

Grabarnik, P., Myllymäki, M. Stoyan, D. (2011). Correct testing of mark independence for marked point patterns. Ecological Modelling 222, 3888-3894.

Myllymäki, M., Mrkvicka, T., Seijo, H., Grabarnik, P. (2013). Global envelope tests for spatial processes. arXiv preprint arXiv:1307.0239.

**18/9, Jean-François Coeurjolly, LJK, Grenoble, Stein's estimation of the intensity of a stationary spatial Poisson point process**

Abstract:

We revisit the problem of estimating the intensity parameter of a homogeneous Poisson point process observed in a bounded window of Rd making use of a (now) old idea of James and Stein. For this, we prove an integration by parts formula for functionals defined on the Poisson space. This formula extends the one obtained by Privault and Réveillac (Statistical inference for Stochastic Processes, 2009) in the one-dimensional case. As in Privault and Réveillac, this formula is adapted to a notion of gradient of a Poisson functional satisfying the chain rule, which is the key ingredient to propose new estimators able to outperform the maximum likelihood estimator (MLE) in terms of the mean squared error.

The new estimators can be viewed as biased versions of the MLE but with a well--constructed bias, which reduces the variance. We study a large class of examples and show that with a controlled probability the corresponding estimator outperforms the MLE. We will illustrate in a simulation study that for very reasonable practical cases (like an intensity of 10 or 20 of a Poisson point process observed in the euclidean ball of dimension between 1 and 5) we can obtain a relative (mean squared error) gain of 20% of the Stein estimator with respect to the maximum likelihood.

This is a joint work with M. Clausel and J. Lelong (Univ. Grenoble).

**2/10,**

**Vadim Shcherbakov, Royal Holloway, University of London, Long term behaviour of locally interacting birth-and-death processes**

Abstract:

In this talk paper we consider the long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A partial description of the asymptotic behaviour in the case of general graphs is given and the cases of both constant vertex degree graphs and star graphs are considered in more details. The model is motivated by modelling interactions between populations, adsorption-desorption processes and is related to interacting particle systems, Gibbs models with unbounded spins, as well as urn models with interaction. Based on joint work with Stanislav Volkov (Lund University).

**16/10, Peter Guttorp, University of Washington, USA, Comparing regional climate models to weather data**

Climate models do not model weather, and there is no way to collect climate data. From a statistical point of view we can define climate as the distribution of weather. That allows us to compare the distribution of output from historical climate model runs (over time and space) to the distribution of weather observations (also over time and space). This type of comparison is made for extreme temperatures at a single site and over a network of sites in Sweden, as well as for precipitation over Norway. The observed temperature distribution can be well described by the output from a regional climate model, but Norwegian precipitation needs to be corrected in order to achieve any reasonable agreement.

**23/10, Tomasz Kozubowski, University of Nevada, USA, Certain bivariate distributions and random processes connected with maxima and minima**

Abstract:

It is well-known that [S(x)]n and [F(x)]n are the survival function and the distribution function of the minimum and the maximum of n independent, identically distributed random variables, where S and F are their common survival and distribution functions, respectively. These two extreme order statistics play important role in countless applications, and are the central and well-studied objects of extreme value theory. In this work we provide stochastic representations for the quantities [S(x)]α and [F(x)]α, where α > 0 is no longer an integer, and construct a bivariate model with these margins. Our constructions and representations involve maxima and minima with a random number of terms. We also discuss generalisations to random process and further extensions. This research was carried jointly with K. Podgorski.

It is well-known that [S(x)]n and [F(x)]n are the survival function and the distribution function of the minimum and the maximum of n independent, identically distributed random variables, where S and F are their common survival and distribution functions, respectively. These two extreme order statistics play important role in countless applications, and are the central and well-studied objects of extreme value theory. In this work we provide stochastic representations for the quantities [S(x)]α and [F(x)]α, where α > 0 is no longer an integer, and construct a bivariate model with these margins. Our constructions and representations involve maxima and minima with a random number of terms. We also discuss generalisations to random process and further extensions. This research was carried jointly with K. Podgorski.

**6/11, Torgny Lindvall, Chalmers, On coupling of certain Markov processes**

Abstract:

The coupling method is particularly powerful when it comes to birth and death processes and diffusions, e.g. We present applications of the method for ergodicity and stochastic monotonicity of such processes, in one and several dimensions.

**13/11, Giacomo Zanella, University of Warwick, UK, Bayesian complementary clustering, MCMC and Anglo-Saxon placenames**

Abstract: Common cluster models for multi-type point processes model the aggregation of points of the same type. In complete contrast, in the study of Anglo-Saxon settlements it is hypothesized that administrative clusters involving complementary names tend to appear. We investigate the evidence for such an hypothesis by developing a Bayesian Random Partition Model based on clusters formed by points of different types (complementary clustering).

As a result we obtain an intractable posterior distribution on the space of matchings contained in a k-partite hypergraph. We apply the Metropolis-Hastings (MH) algorithm to sample from this posterior. We consider the problem of choosing an efficient MH proposal distribution and we obtain consistent mixing improvements compared to the choices found in the literature. Simulated Tempering techniques can be used to overcome multimodality and a multiple proposal scheme is developed to allow for parallel programming. Finally, we discuss results arising from the careful use of convergence diagnostic techniques.

This allows us to study a dataset including locations and placenames of 1319 Anglo-Saxon settlements dated between 750 and 850 AD. Without strong prior knowledge, the model allows for explicit estimation of the number of clusters, the average intra-cluster dispersion and the level of interaction among placenames. The results support the hypothesis of organization of settlements into administrative clusters based on complementary names.

**27/11, Jennifer Wadsworth, University of Cambridge, Likelihood-based inference for max-stable processes: some recent developments**

Abstract:

Max-stable processes are an important class of models for extreme values of processes indexed by space and / or time. They are derived by taking suitably scaled limits of normalized pointwise maxima of stochastic processes; in practice therefore one uses them as models for maxima over many repetitions. However, the complicated nature of their dependence structures means that full (i.e., d-dimensional, where a process is observed at d locations) likelihood inference is not straightforward. Recent work has demonstrated that by including information on when the maxima occurred, full likelihood-based inference is possible for some classes of models. However, whilst this approach simplifies the likelihood enough to make the inference feasible, it can also cause or accentuate bias in parameter estimation for processes that are weakly dependent. In this talk I will describe the ideas behind full likelihood inference for max-stable processes, and discuss how this bias can occur. Understanding of the bias issue helps to identify potential solutions, and I will illustrate one possibility that has been successful in a high-dimensional multivariate model.

Max-stable processes are an important class of models for extreme values of processes indexed by space and / or time. They are derived by taking suitably scaled limits of normalized pointwise maxima of stochastic processes; in practice therefore one uses them as models for maxima over many repetitions. However, the complicated nature of their dependence structures means that full (i.e., d-dimensional, where a process is observed at d locations) likelihood inference is not straightforward. Recent work has demonstrated that by including information on when the maxima occurred, full likelihood-based inference is possible for some classes of models. However, whilst this approach simplifies the likelihood enough to make the inference feasible, it can also cause or accentuate bias in parameter estimation for processes that are weakly dependent. In this talk I will describe the ideas behind full likelihood inference for max-stable processes, and discuss how this bias can occur. Understanding of the bias issue helps to identify potential solutions, and I will illustrate one possibility that has been successful in a high-dimensional multivariate model.

**2/12, David Perrett, Perception Lab, St Andrews University, UK: Statistical analysis of visual cues underlying facial attractiveness**

Abstract:

Our approach involves two phases: (a) identify visual cues correlated with judgments, (b) confirm the impact of those cues on perception by transforming cue values in images or models of faces. We also search for the biological basis or meaning of the cues. I will illustrate the approaches for how skin colour and 3-D face shape affect perception.

Attractiveness of natural facial images is positively correlated with skin yellowness. Carotenoid pigments from fruit and vegetables in our diet impart yellowness (or ‘golden glow’) to the skin: eating more fruit and vegetables is accompanied by an increase in skin yellowness within a few weeks. Transforming facial images simulating an increase in the colour associated with a high carotenoid diet increases the apparent health and attractiveness of most faces. These judgments hold across cultures and ages (from early childhood to late adulthood). Carotenoid ornaments are used in many species as a signal of health, and are sexually selected. In humans too we find that carotenoid colour may provide an index of wellbeing in terms of fitness, and resilience to illness.

To analyse face shape we record a depth map of individual faces. For each face we manually define the position of 50 3-D landmarks (e.g., eye corners) on the depth map and then resample the facial surface so that there are a standard number of vertices between landmarks. Next the dimensions of surface shape variation across different faces are reduced using Principal Components Analysis. The vector between the average male face shape and average female face shape defines an axis of sexual dimorphism (or femininity – masculinity). Transforming the shape of faces along this axis, we find a curvilinear (quadratic) relationship of women’s ratings of attractiveness to men’s facial masculinity, with a peak in attractiveness at +90% shape masculinity and aversion to very low and very high levels of masculinity. This research work shows higher levels of masculinity to be attractive than prior work on the shape of faces using in 2-D images possibly because of the importance of volumetric details and increased realism of 3-D head models.

Other topics to be discussed include the role of (over) generalization in perceptual judgments to specific face cues and non-uniform 3-D facial growth.

**4/12, Anna Kiriliouk, Université Catholique de Louvain, An M-estimator of spatial tail dependence**

Abstract: Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank-based M-estimator is proposed relying on bivariate margins only. A data-driven weight matrix is used to minimize the asymptotic variance. Empirical process arguments show that the estimator is consistent and asymptotically normal. Its finite-sample performance is assessed in simulation experiments involving popular max-stable processes perturbed with additive noise. An analysis of wind speed data from the Netherlands illustrates the method.

**11/12, Nibia Aires, Astellas Pharma, Leiden, Statistics in drug development, what happens after submission?**

Abstract:

In drug development, a new candidate compound with potential good properties to cure a disease condition needs to go through a long path to become a new medicine, new medical treatment or device. Starting at an exploratory phase where, for instance, a new molecule is identified and tested in a range of settings; it continues, if successful, to an early clinical development phase being tested in humans. At this stage, if its toxicity and patient safety is established successfully, the new compound will follow a series of testing in controlled experiments involving humans, so called clinical trials, with the goal to launch the new drug to the market.

In drug development, a new candidate compound with potential good properties to cure a disease condition needs to go through a long path to become a new medicine, new medical treatment or device. Starting at an exploratory phase where, for instance, a new molecule is identified and tested in a range of settings; it continues, if successful, to an early clinical development phase being tested in humans. At this stage, if its toxicity and patient safety is established successfully, the new compound will follow a series of testing in controlled experiments involving humans, so called clinical trials, with the goal to launch the new drug to the market.

However, after submission, and even after the new drug has been approved by the health authorities, the investigation process is not yet finalized. Additional studies, sometimes called late phase studies, might be required with the purpose of assessing long-term safety, or evaluate the new treatment in a real world setting or to address particular questions for its commercialization in a market as a result of a Health Technology Assessment.

These studies in many cases are observational, where subjects are followed by a determined period of time but the assignment of the subject to a treatment is outside of the control of the investigator.

In this talk, I will focus on observational studies in drug development, which involve specific statistical methodology for the design and analysis. I will also briefly describe the process for commercialization approval, Health Technology Assessments and Post Authorisation Safety Studies.

**16/12, Sören Christensen, Kiel, Representation Results for Excessive Functions and Application to Stochastic Control Problems**

Abstract:

Two approaches for solving sequential decision problems are presented. Both are based on representation results for excessive functions of Markov processes. In the first approach, we represent these functions as expected suprema up to an exponential time. This leads to generalizations of recent findings for Lévy processes obtained essentially via the Wiener-Hopf factorization to general strong Markov processes on the real line. In the second approach, the Riesz integral representation is utilized to solve sequential decision problems without the machinery of local time-space-calculus on manifolds. In the end, generalizations of these findings to impulse control problems are discussed.

Most results are based on joint work with Paavo Salminen.

**18/12, Mark van de Wiel, Dep. of Epidemiology & Biostatistics and Dep. of Mathematics, VU University medical center and VU university, How to learn from a lot: Empirical Bayes in Genomics**

Abstract:

The high-dimensional character of genomics data generally forces statistical inference methods to apply some form of penalization, e.g. multiple testing, penalized regression or sparse gene networks. The other side of the coin, however, is that the dimension of the variable space may also be used to learn across variables (like genes, tags, methylation probes, etc). Empirical Bayes is a powerful principle to do so. In both Bayesian and frequentist applications it comes down to estimation of the a priori distribution of parameter(s) from the data.

We shortly review some well-known statistical methods that use empirical Bayes to analyse genomics data. We believe, however, that the principle is often not used at its full strength. We illustrate the flexibility and versatility of the principle in three settings: 1) Bayesian inference for differential expression from count data (e.g. RNAseq), 2) prediction of binary response, and 3) network reconstruction.

For 1) we develop a novel algorithm, ShrinkBayes, for the efficient simultaneous estimation of multiple priors, allowing joint shrinkage of multiple parameters in differential gene expression models. This can be attractive when sample sizes are small or when many nuisance parameters like batch effects are present. For 2) we demonstrate how auxiliary information in the form of 'co-data', e.g. p-values from an external study or genomic annotation, can be used to improve prediction of binary response, like tumour recurrence. We derive empirical Bayes estimates of penalties of groups of variables in a classical logistic ridge regression setting, and show that multiple source of co-data may be used. Finally, for 3) we combine empirical Bayes with computationally efficient variational Bayes approximations of posteriors for the purpose of gene network reconstruction by the use structural equation models. These models regress each gene on all others, and hence this setting can be regarded as a combination of 1) and 2). We show the benefits of empirical Bayes on a several real data sets.

**18/12,**

**Lars Rönnegård, Dalarna University: Hierarchical generalized linear models – a Lego approach to mixed models**

Abstract: The method of hierarchical generalized linear models (HGLM) fits generalized linear models with random effects and was introduced by Lee & Nelder (1996). It is based on the extended likelihood principle and is a complete statistical framework including inference and model selection tools. In this presentation I give several examples from genetics where HGLM has been applied. I will also show that the HGLM approach allows extended modelling in a building-block type of structure; like Lego. Together with my colleagues, I have implemented the HGLM method in the R package hglm (available on CRAN) and I will show how this “Lego approach” can be used to fit quantitative genetic models and spatial CAR models in hglm.

## 2013

**31/1, Mikhail Lifshits, S:t Petersburg State University: Small deviation probabilities and their interplay with operator theory and bayesian statistics**

Abstract:

Small deviation, or small ball, probability simply means P(||X||<r) as r tends to zero for X being a random element of a Banach space. Typically X is a trajectory of a random process such as Wiener process, fractional Brownian motion, Levy process, etc., while ||.|| is some norm on a functional space. There is no general technique for evaluating small deviation probability but in some important cases interesting links lead from small deviations to entropy of linear operators, eigenvalues of Sturm-Liouville problems etc. We will discuss these links, supply examples, and will review some applications to Bayesian statistics.

Small deviation, or small ball, probability simply means P(||X||<r) as r tends to zero for X being a random element of a Banach space. Typically X is a trajectory of a random process such as Wiener process, fractional Brownian motion, Levy process, etc., while ||.|| is some norm on a functional space. There is no general technique for evaluating small deviation probability but in some important cases interesting links lead from small deviations to entropy of linear operators, eigenvalues of Sturm-Liouville problems etc. We will discuss these links, supply examples, and will review some applications to Bayesian statistics.

**14/3, Anders Sandberg, Future of Humanity Institute, Oxford, Probing the Improbable: Methodological Challenges for Risks with Low Probabilities and High Stakes**

Abstract:

Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calculations often put very low probabilities on the occurrence of such catastrophes. In this paper, we argue that there are important new methodological problems which arise when assessing global catastrophic risks and we focus on a problem regarding probability estimation. When an expert provides a calculation of the probability of an outcome, they are really providing the probability of the outcome occurring, given that their argument is watertight. However, their argument may fail for a number of reasons such as a flaw in the underlying theory, a flaw in the modeling of the problem, or a mistake in the calculations. If the probability estimate given by an argument is dwarfed by the chance that the argument itself is flawed, then the estimate is suspect. We develop this idea formally, explaining how it differs from the related distinctions of model and parameter uncertainty. Using the risk estimates from the Large Hadron Collider as a test case, we show how serious the problem can be when it comes to catastrophic risks and how best to address it. This is joint work with Toby Ord and Rafaela Hillerbrand.

Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calculations often put very low probabilities on the occurrence of such catastrophes. In this paper, we argue that there are important new methodological problems which arise when assessing global catastrophic risks and we focus on a problem regarding probability estimation. When an expert provides a calculation of the probability of an outcome, they are really providing the probability of the outcome occurring, given that their argument is watertight. However, their argument may fail for a number of reasons such as a flaw in the underlying theory, a flaw in the modeling of the problem, or a mistake in the calculations. If the probability estimate given by an argument is dwarfed by the chance that the argument itself is flawed, then the estimate is suspect. We develop this idea formally, explaining how it differs from the related distinctions of model and parameter uncertainty. Using the risk estimates from the Large Hadron Collider as a test case, we show how serious the problem can be when it comes to catastrophic risks and how best to address it. This is joint work with Toby Ord and Rafaela Hillerbrand.

**4/4, Daniel Johansson, Fysisk resursteori, Chalmers: Climate sensitivity: Learning from observations**

Abstract:

Although some features of climate change are known with relative certainty, many uncertainties in the climate science remain. The most important uncertainty pertains to the Climate Sensitivity (CS), i.e., the equilibrium increase in the global mean surface temperature that follows from a doubling of the atmospheric CO2 concentration. A probability distribution for the CS can be estimated from the observational record of global mean surface temperatures and ocean heat uptake together with estimates of anthropogenic and natural radiative forcings. However, since the CS is statistically dependent on other uncertain factors, such as the uncertainty in the direct and indirect radiative forcing of aerosols, it is difficult to constrain this distribution from observations. The primary aim with this presentation is to analyse how the distribution of the climate sensitivity changes over time as the observational record becomes longer. We are using a Bayesian Markov Chain Monte Carlo approach together with an Upwelling Diffusion Energy Balance Model for this. Also, we will discuss in brief how sensitive the climate sensitivity estimate is to changes in the structure of the geophysical model and to changes on the observational time series.

Although some features of climate change are known with relative certainty, many uncertainties in the climate science remain. The most important uncertainty pertains to the Climate Sensitivity (CS), i.e., the equilibrium increase in the global mean surface temperature that follows from a doubling of the atmospheric CO2 concentration. A probability distribution for the CS can be estimated from the observational record of global mean surface temperatures and ocean heat uptake together with estimates of anthropogenic and natural radiative forcings. However, since the CS is statistically dependent on other uncertain factors, such as the uncertainty in the direct and indirect radiative forcing of aerosols, it is difficult to constrain this distribution from observations. The primary aim with this presentation is to analyse how the distribution of the climate sensitivity changes over time as the observational record becomes longer. We are using a Bayesian Markov Chain Monte Carlo approach together with an Upwelling Diffusion Energy Balance Model for this. Also, we will discuss in brief how sensitive the climate sensitivity estimate is to changes in the structure of the geophysical model and to changes on the observational time series.

**11/4, Johan Johansson, Chalmers: On the BK inequality**

Abstract:

A family of binary random variables is said to have the BK property if, loosely speaking, for any two events that are increasing in the random variables, the probability that they occur disjointly is at most the product of the probabilities of the two events. The classical BK inequality states that this holds if the random variables are independent. Since the BK property is stronger than negative association, it is a form of negative dependence property and one would expect other negatively dependent families to have the BK property. This has turned out to be quite a challenge and until very recently, no substantial example beside the independent case were known. In this talk I will give two of these examples, the k-out-of-n measure and pivotal sampling, and sketch how to prove the BK inequality for these. I will also mention a few seemingly "simple questions" and how solutions to these would be profoundly important.

A family of binary random variables is said to have the BK property if, loosely speaking, for any two events that are increasing in the random variables, the probability that they occur disjointly is at most the product of the probabilities of the two events. The classical BK inequality states that this holds if the random variables are independent. Since the BK property is stronger than negative association, it is a form of negative dependence property and one would expect other negatively dependent families to have the BK property. This has turned out to be quite a challenge and until very recently, no substantial example beside the independent case were known. In this talk I will give two of these examples, the k-out-of-n measure and pivotal sampling, and sketch how to prove the BK inequality for these. I will also mention a few seemingly "simple questions" and how solutions to these would be profoundly important.

**16/4, Alexandra Jauhiainen: Inferring Regulatory Networks by Combining Perturbation Screens and Steady State Gene Expression Profiles**

Abstract:

Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction problem. However, such data can be limited in size and/or expensive to acquire. On the other hand, observational data of the organism in steady state (e.g. wild-type) are more readily available, but their informational content is inadequate for the task at hand. We develop a computational approach to appropriately utilize both data sources for estimating a regulatory network.

The proposed approach is based on a three-step algorithm to estimate the underlying directed but cyclic network, that uses as input both perturbation screens and steady state gene expression data. In the first step, the algorithm determines causal orderings of the genes that are consistent with the perturbation data, by combining an exhaustive search method with a fast heuristic that in turn couples a Monte Carlo technique with a fast search algorithm. In the second step, for each ordering, a regulatory network is estimated using a penalized likelihood based method, while in the third step a consensus network is constructed from the highest scored ones. Extensive computational experiments show that the algorithm performs well in uncovering the underlying network and clearly outperforms competing approaches that rely only on a single data source. Further, it is established that the algorithm produces a consistent estimate of the regulatory network.

Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction problem. However, such data can be limited in size and/or expensive to acquire. On the other hand, observational data of the organism in steady state (e.g. wild-type) are more readily available, but their informational content is inadequate for the task at hand. We develop a computational approach to appropriately utilize both data sources for estimating a regulatory network.

The proposed approach is based on a three-step algorithm to estimate the underlying directed but cyclic network, that uses as input both perturbation screens and steady state gene expression data. In the first step, the algorithm determines causal orderings of the genes that are consistent with the perturbation data, by combining an exhaustive search method with a fast heuristic that in turn couples a Monte Carlo technique with a fast search algorithm. In the second step, for each ordering, a regulatory network is estimated using a penalized likelihood based method, while in the third step a consensus network is constructed from the highest scored ones. Extensive computational experiments show that the algorithm performs well in uncovering the underlying network and clearly outperforms competing approaches that rely only on a single data source. Further, it is established that the algorithm produces a consistent estimate of the regulatory network.

**2/5, Maryam Zolghadr and Sergei Zuyev, Chalmers: Optimal design of dilution experiments under volume constraints**

Abstract:

We develop methods to construct a one-stage design of dilution experiments under the total available volume constraint typical for bio-medical applications. We consider different optimality criteria based on the Fisher information in both non-Bayesian and Bayesian settings. It turns out that the optimal design is typically one atomic, meaning that all the dilutions should be of the same size. Our proposed approach to solve such optimization problems is a variational analysis of functionals of a measure. The advantage of the measure optimization approach is that additional requirements like a total cost of experiment can be easily incorporated into the goal function.

**21/5, Johan Wallin, Lund: Spatial Matérn fields generated by non-Gaussian noise**

Abstract:

In this work, we study non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations, and Gaussian Markov random fields. We show how to construct efficient representations of non-Gaussian random fields generated by generalized asymmetric Laplace noise and normal inverse Gaussian noise, and discuss parameter estimation and spatial prediction for these models. Finally, we look at an application to precipitation data from the US.

**23/5, Youri Davydov, Université Lille-1: On convex hulls of sequences of stochastic processes**

Abstract:

Let X_i = { X_i (t), t in T} be i.i.d. copies of a d-dimensional process X = { X(t), \; t in T}, where T is a general separable metric space. Assume that X has a.s. bounded paths and consider the convex hulls W_n constructed by the trajectories of X_i's. We are studying the existence of a limit shape W for the sequence {W_n} normalised by appropriate constants b_n. We show that in the case of Gaussian processes, W_n/b_n converges a.s. to W which is nonrandom, whereas for the processes satisfying a regular variation condition the convergence is in law and the limit set W in many cases is a random polytope.

**28/5, Patrik Rydén, Department of Mathematics and Mathematical statistics and Computational Life science Cluster (CLiC), Umeå University: Analysis of high-dimensional genomics data - challenges and opportunities**

Abstract:

High throughput technologies in life science such as high-throughput DNA and RNA sequencing, gene expression arrays, mass spectrometry, ChIP-chip and methylation arrays have allowed genome-wide measurements of complex cellular responses for a broad range of treatments and diseases. The modern technologies are powerful, but in order for them to reach their full potential new statistical tools need to be developed.

I will discuss pre-processing of microarray data (the discussion will also be relevant for other techniques), how pre-processing affects down-stream cluster analysis and why cluster analysis of samples (e.g. tumour samples) often fails to cluster the samples in a relevant manner. Finally, I will give my view on the future in the field of genomics research and what role statisticians can play.

**13/6, Fima Klebaner, Evaluations of expectations of functionals of diffusions by simulations**

Abstract:

We consider the problem of evaluations of expectations by simulations. After a brief introduction, we point out that there is a problem with the standard approach if the functional in question is not continuous. Evaluation of probability of absorption (or ruin probability) by simulations is shown as an example. We give a modification of the standard Euler-Maruyama scheme to obtain convergence. Open problems still remain. This joint work with Pavel Chigansky, Hebrew University.

**29/8, Jesper Möller, Aalborg University, Determinantal point process models and statistical inference**

Abstract:

Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored, though they possess a number of appealing properties and have been studied in mathematical physics, combinatorics, and random matrix theory. We demonstrate that DPPs provide useful models for the description of repulsive spatial point processes, particularly in the 'soft-core' case. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We exploit the appealing probabilistic properties of DPPs to develop parametric models, where the likelihood and moment expressions can be easily evaluated and realizations can be quickly simulated. We discuss how statistical inference is conducted using the likelihood or mo- ment properties of DPP models, and we provide freely available software for simulation and statistical inference.

The work has been carried out in collaboration with Ege Rubak, Aalborg University, and Frederic Lavancier, University of Nantes. The paper is available at arXiv:1205.4818.

Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored, though they possess a number of appealing properties and have been studied in mathematical physics, combinatorics, and random matrix theory. We demonstrate that DPPs provide useful models for the description of repulsive spatial point processes, particularly in the 'soft-core' case. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We exploit the appealing probabilistic properties of DPPs to develop parametric models, where the likelihood and moment expressions can be easily evaluated and realizations can be quickly simulated. We discuss how statistical inference is conducted using the likelihood or mo- ment properties of DPP models, and we provide freely available software for simulation and statistical inference.

The work has been carried out in collaboration with Ege Rubak, Aalborg University, and Frederic Lavancier, University of Nantes. The paper is available at arXiv:1205.4818.

**12/9, Christos Dimitrakakis, Chalmers, ABC Reinforcement Learning**

Abstract:

We introduces a simple, general framework for \emph{likelihood-free} Bayesian reinforcement learning, through Approximate Bayesian Computation (ABC). The main advantage is that we only require a prior distribution on a class of simulators. This is useful in domains where a probabilistic model of the underlying process is too complex to formulate, but where detailed simulation models are available. ABC-RL allows the use of any Bayesian reinforcement learning technique in this case. In fact, it can be seen as an extension of simulation methods to both planning and inference.

We experimentally demonstrate the potential of this approach in a comparison with LSPI. Finally, we introduce a theorem showing that ABC is sound.

**19/9, Jeff Steif, Strong noise sensitivity and Erdos Renyi random graphs**

Abstract: Noise sensitivity concerns the question of when complicated events involving many i.i.d. random variables are (or are not) sensitive to small perturbations in these variables.

The Erdos Renyi random graph is the graph obtained by taking n vertices and connecting each pair of vertices independently with probability p_n.

This random graph displays very interesting behaviour. We will discuss some recent results concerning noise sensitivity for events involving the Erdos Renyi random graph. This is joint work with Eyal Lubetzky.

**24/9, Ben Morris, University of California, Mixing time of the card-cyclic to random shuffle**

Abstract: We analyse the following method for shuffling n cards. First, remove card 1 (i.e., the card with label 1) and then re-insert it randomly into the deck. Then repeat with cards 2, 3,..., n. Call this a round. R. Pinsky showed, somewhat surprisingly, that the mixing time is greater than one round. We show that in fact the mixing time is on the order of log n rounds. Joint work with Weiyang Ning and Yuval Peres.

**26/9,**

**Ben Morris, University of California, Mixing time of the overlapping cycles shuffle and square lattice rotations shuffle**

Abstract: The overlapping cycles shuffle, invented by Johan Jonasson, mixes a deck of n cards by moving either the nth card or (n-k)th card to the top of the deck, with probability half each. Angel, Peres and Wilson determined the spectral gap for the location of a single card and found the following surprising behaviour. Suppose that k is the closest integer to cn for a fixed c in (0,1). Then for rational c, the spectral gap is on the order of n^{-2}, while for poorly approximable irrational numbers c, such as the reciprocal of the golden ratio, the spectral gap is on the order of n^{-3/2}. We show that the mixing time for all the cards exhibits the same behaviour (up to logarithmic factors), proving a conjecture of Jonasson.

The square lattice rotations shuffle, invented by Diaconis, is defined as follows. The cards are arrayed in a square. At each step a row or column is chosen, uniformly at random, and then cyclically rotated by one unit. We find the mixing time of this shuffle to within logarithmic factors. Joint work with Olena Blumberg.

**3/10, Malwina Luczak, Queen Mary, University of London, The stochastic logistic epidemic**

Abstract: This talk concerns one of the simplest and most studied models of the spread of an epidemic within a population. The model has two parameters, the infection rate and the recovery rate, and the behaviour is very different depending on which is larger. We focus on the case where the recovery rate is greater, when the epidemic is doomed to die out quickly. But exactly how quickly turns out to be a thorny problem.

(joint work with Graham Brightwell)

(joint work with Graham Brightwell)

**10/10, Johan Tykesson, The Poisson cylinder model**

Abstract:

We consider a Poisson point process on the space of lines in R^d, where a multiplicative factor u>0 of the intensity measure determines the density of lines. Each line in the process is taken as the axis of a bi-infinite solid cylinder of radius 1. We show that there is a phase transition in the parameter u regarding the existence of infinite connected components in the complement of the union of the cylinders. We also show that given any two cylinders c_1 and c_2 in the process, one can find a sequence of d-2 other cylinders which creates a connection between c_1 and c_2.

The talk is based on joint works with Erik Broman and David Windisch.

**15/10,**

**Manuel García Magariños, UDC, Spain, A new parametric approach to kinship testing**

Abstract:

Determination of family relationships from DNA data goes back decades. Statistical inference of relationships has traditionally followed a likelihood-based approach. In the forensic science, hypothesis testing is usually formulated verbally in order to provide with a good understanding to non-experts. Nonetheless, this formulation lacks a proper mathematical parameterization, leading to controversy in the field. We propose an alternative hypothesis testing framework based on the likelihood calculations for pairwise relationships of Thompson, 1975. This is in turn based on the concept of identity-by-descent (IBD) genes shared between individuals. Pairwise relationships can be specified by (k0,k1,k2), the probability that two individuals share 0, 1 and 2 IBD alleles. The developed approach allows to build a complete framework in statistical inference: point estimation, hypothesis testing and confidence regions for (k0,k1,k2). Theoretical properties have been studied. Extension to trios has been carried out in order to consider common problems in forensics. Results indicate the hypothesis testing procedure is quite powerful, especially with trios. Accurate point estimations of (k0,k1,k2) are obtained. This holds even for low number of markers and intricate relationships. Extensions to more than three individuals and inbreeding cases remain to be developed.

**17/10 kl 13.15-14.30, Tanja Stadler, ETH, Phylogenetics in action: Uncovering macro-evolutionary and epidemiological dynamics based on molecular sequence data**

Abstract:

What factors determine speciation and extinction dynamics? How can we explain the spread of an infectious disease? In my talk, I will discuss computational advances in order to address these key questions in the field of macro-evolution and epidemiology. In particular, I will present phylogenetic methodology to infer (i) macro-evolutionary processes based on species phylogenies shedding new light on mammal and bird diversification, and (ii) epidemiological processes based on genetic sequence data from pathogens shedding new light on the spread of HCV and HIV.

**17/10, Gordon Slade, University of British Columbia, Weakly self-avoiding walk in dimension four**

Abstract: We report on recent and ongoing work on the continuous-time weakly self-avoiding walk on the 4-dimensional integer lattice, with focus on a proof that the susceptibility diverges at the critical point with a logarithmic correction to mean-field scaling. The method of proof, which is of independent interest, is based on a rigorous renormalisation group analysis of a supersymmetric field theory representation of the weakly self-avoiding walk. The talk is based on collaborations with David Brydges, and with Roland Bauerschmidt and David Brydges.

**22/10, Prof. Gennady Martynov, Inst. for Information Transmission Problems, RAS, Moscow: Cramer-von Mises Gaussianity test for random processes on [0,1]**

Abstract. We consider the problem of testing the hypothesis that the observed in the interval (0,1) is a Gaussian random process. Representation of the process in the Hilbert space it is used . The proposed test is based on the classic Cramer-von Mises test. We introduce also a modification of the concept of the distribution function. It was developed an asymmetric Cramer-von Mises test. The methods must be considered for exact calculation of limiting distributions tables of the proposed statistics.

**31/10, Alexandre Proutiere, KTH, Bandit Optimisation with Large Strategy Sets and Applications**

Abstract: Bandit optimisation problems constitute the most fundamental and basic instances of sequential decision problems with an exploration-exploitation trade-off. They naturally arise in many contemporary applications found in communication networks, e-commerce and recommendation systems. In this lecture, we present recent results on bandit optimisation problems with large strategy sets. For such problems, the number of possible strategies may not be negligible compared to the time horizon. Results are applied to the design of protocols and resource sharing algorithms in wireless systems.

**7/11,**

**Boualem Djehiche, KTH, On the subsolution approach to efficient importance sampling**

Abstract: The widely used Monte Carlo simulation technique where all the particles are independent and statistically identical and their weights are constant is by no means universally applicable. The reason is that particles may wander off to irrelevant parts of the state space, leaving only a small fraction of relevant particles that contribute to the computational task at hand. Therefore it may require a huge number of particles to obtain a desired precision, resulting in a computational cost that is too high for all practical purposes. A control mechanism is needed to force the particles to move to the relevant part of the space, thereby increasing the importance of each particle and reducing the computational cost. Importance sampling technique offers a way to choose a sampling dynamics (the main difficult part) to steer the particles towards the relevant part of the state space. In this talk I will review some recent results on the so-called subsolution approach to Importance Sampling that is able to tune the sampling dynamics at hopefully lower costs.

This is joint work with Henrik Hult and Pierre Nyquist.

**12/11, Ioannis Papastathopoulos, Bristol University, Graphical structures in extreme multivariate events**

Abstract: Modelling and interpreting the behaviour of extremes is quite challenging, especially when the dimension of the problem under study is large. Initially, univariate extreme value models are used for marginal tail estimation and then, the inter-relationships between random variables are captured by modelling the dependence of the extremes. Here, we propose graphical structures in extreme multivariate events of a random vector given that one of its components is large. These structures aim to provide better estimates and predictions of extreme quantities of interest as well as to reduce the problems with the curse of dimensionality. The imposition of graphical structures in the estimation of extremes is approached via simplified parameter structure in maximum likelihood setting and through Monte Carlo simulation from conditional kernel densities. The increase in efficiency of the estimators and the benefits of the proposed method are illustrated through simulation studies.

**21/11, Annika Lang, How does one computationally solve a stochastic partial differential equation?**

Abstract:

The solution of a stochastic partial differential equation can for example be seen as a Hilbert-space-valued stochastic process. In this talk I discuss discretizations in space, time, and probability to simulate the solution with a computer and I derive convergence rates for different types of approximation errors.

**28/11 Arne Pommerening, Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Birmensdorf, Switzerland What are the differences between competition kernels and traditional size-ratio based competition indices used in plant ecology?**

Abstract: Both traditional competition indices and competition kernels are used in many studies to quantify competition between plants for resources. Yet it is not fully clear what the differences between these two concepts really are.

For a fair comparison of the two approaches we selected two fundamental and widespread types of competition indices based on distance weighted size ratios, an additional index without distance weighting as a control and developed the corresponding competition kernels. In contrast to the latter, competition indices require individual influence zones derived from tree crown-radius measurements. We applied these competition measures to three spatial tree time series in forest ecosystems in Europe and North America. Stem diameter increment served as a response variable.

Contrary to our expectation, the results of both methods indicated similar performance, however, the use of competition kernels produced slightly better results with only one exception out of six comparisons.

Although the performance of both competition measures is not too different, competition kernels are based on more solid mathematical and ecological grounds. This is why applications of this method are likely to increase. The trade-off of the use of competition kernels, however, is the need for more sophisticated spatial regression routines that researchers are required to program.

For a fair comparison of the two approaches we selected two fundamental and widespread types of competition indices based on distance weighted size ratios, an additional index without distance weighting as a control and developed the corresponding competition kernels. In contrast to the latter, competition indices require individual influence zones derived from tree crown-radius measurements. We applied these competition measures to three spatial tree time series in forest ecosystems in Europe and North America. Stem diameter increment served as a response variable.

Contrary to our expectation, the results of both methods indicated similar performance, however, the use of competition kernels produced slightly better results with only one exception out of six comparisons.

Although the performance of both competition measures is not too different, competition kernels are based on more solid mathematical and ecological grounds. This is why applications of this method are likely to increase. The trade-off of the use of competition kernels, however, is the need for more sophisticated spatial regression routines that researchers are required to program.

(2011). Correct testing of mark independence for marked point patterns. Ecological Modelling 222, 3888-3894.

**5/12, Kaspar Stucki, University of Göttingen, Germany, Continuum percolation for Gibbs point processes**

Abstract:

We consider percolation properties of the Boolean model generated by a Gibbs point process and balls with deterministic radius. We show that for a large class of Gibbs point processes there exists a critical activity, such that percolation occurs a.s. above criticality. For locally stable Gibbs point processes we show a converse result, i.e. they do not percolate a.s. at low activity.

**12/12, Olle Häggström, Are all ravens black? The problem of induction**

How do we draw conclusions about what we have not yet seen based on what we have seen? That is the age-old problem of induction. Statistical inference is meant to solve it, but does it? In this talk I will give a brief and selective review of the history of the problem, and discuss where we stand today.

**19/12, Marianne Månsson, Astra Zeneca, Statistical paradoxes and curiosities in medical applications**

Abstract:

Why do my friends have more friends than I have? A feeling shared by most people which was formulated in the 90s as The friendship paradox. Is it really true? Can it be used for prediction of epidemics? This is one of the paradoxes which will be discussed in this seminar.

## 2012

**19/1 Anna-Kaisa Ylitalo, University of Jyväskylä, Statistical inference for eye movements**

Abstract:

Eye movements can be measured by electronic eye trackers, which produce high-precision spatio-temporal data. Eye tracking has become an important and widespread indirect measure of reactions to stimuli both in planned experiments and in observational studies. In applications mainly conventional statistical methods have been used for the analysis of eye tracking data and often the methods are based on strong aggregation. Our aim is to utilize more advanced statistical approaches through modelling in order to extract detailed information on the data. The great challenges are heterogeneity and large variation within and between the units.

Eye movements can be measured by electronic eye trackers, which produce high-precision spatio-temporal data. Eye tracking has become an important and widespread indirect measure of reactions to stimuli both in planned experiments and in observational studies. In applications mainly conventional statistical methods have been used for the analysis of eye tracking data and often the methods are based on strong aggregation. Our aim is to utilize more advanced statistical approaches through modelling in order to extract detailed information on the data. The great challenges are heterogeneity and large variation within and between the units.

The eye movement data are usually heterogeneous in time and space and not extensive. Hence approaching the statistical problem in full generality is perhaps too ambitious. Reductions or simplifications are necessary. We have two main approaches: space or time reduction. In this case we concentrate to the spatial nature of the data and hence the time aspect is reduced. That leads to the presentation of eye movement data as marked point patterns.

Statistically thinking, a fixation location can be treated as a point in the plain and fixation duration as a mark for that point. Hence a set of fixations constitute a marked point pattern, or more specify, an ordered marked point pattern. The family of point processes offers a wide range of statistics, which can now be used for eye movement data analysis.

In addition, the targets can vary from weakly spatially structured (art, medical images) to strongly structured (reading, music reading) which may lead to different type of data reduction and modelling. One of the aims is that the methods suggested have to be applicable in both of the cases.

The main result of this study consists of new statistical tools for describing and summarizing the eye movement process. For example, convex hull for illustrating the spatial dispersion of the fixations. These tools can be used for feature extraction and classification of the data and hence group comparisons are feasible. In eye movement applications the group comparison is a major area of interest. Another interesting approach is the case-control study, in which a selection of control is a major dilemma.

**26/1 Chris Jennison, University of Bath, Effective design of Phase II and Phase III trials: an over-arching approach**

Abstract:

This talk will report on work carried out by a DIA (formerly PhRMA) Working Group on Phase II/III Adaptive Programs.

This talk will report on work carried out by a DIA (formerly PhRMA) Working Group on Phase II/III Adaptive Programs.

We consider the joint design of Phase II and Phase III trials. Our aim is to optimise the gain from a successful Phase III trial, allowing for the costs incurred in achieving this. Our model reflects the uncertainties faced when a company makes decisions on whether or not to run a Phase III trial for a new drug and, if so, which dose to take forward from Phase II and how large a Phase III study to conduct.

We follow a Bayes decision theoretic approach, starting with a prior distribution for the parameters in a dose response model, adding costs of sampling in Phase II and Phase III, and ending with a gain function for a positive Phase III outcome. This gain can be discounted by the loss of patent lifetime while trials are carried out. We also incorporate a risk curve for the probability that each dose should fail on safety grounds.

It is a challenging problem to optimise jointly the study design for comparing doses in Phase II, the rule for choosing a dose or doses to progress to Phase III, and the Phase III design itself. We show that it is feasible to tackle this problem and we discuss generalisations from an initial, simple formulation.

While the statistical models, prior probabilities, and utilities needed in our approach may be difficult to elicit, it is clear that decisions are currently made which should really be informed by these inputs. Other sub-groups of the Working Group have explored more detailed formulations of our problem in specific therapeutic areas, complementing the generic methodology to be presented in this talk.

**7/2, Paavo Salminen, Åbo Akademi, Optimal stopping of continuous time Markov processes**

Abstract:

After two motivating examples some methods/verification theorems for solving optimal stopping problems will be discussed. These are based on

- principle of smooth pasting,

- Riesz representation for excessive functions,

- representing excessive functions as expected supremum.

The talk is concluded with further examples, in particular, for Lévy processes

After two motivating examples some methods/verification theorems for solving optimal stopping problems will be discussed. These are based on

- principle of smooth pasting,

- Riesz representation for excessive functions,

- representing excessive functions as expected supremum.

The talk is concluded with further examples, in particular, for Lévy processes

**7/2, Juha Alho, University of Eastern Finland, Statistical aspects of mortality modeling**

Abstract:

Declines of mortality have, during the past century, been clearly faster than anticipated. Mistaken judgment has been the primary reason for erroneous forecasts, but decisions made in statistical modeling can also play a remarkably large role. We will illustrate the problem with data and experiences from Sweden and other countries and comment on the implications on the sustainability of pension systems. In particular, the Finnish life expectancy adjustment and the Swedish NDC system will be mentioned.

Declines of mortality have, during the past century, been clearly faster than anticipated. Mistaken judgment has been the primary reason for erroneous forecasts, but decisions made in statistical modeling can also play a remarkably large role. We will illustrate the problem with data and experiences from Sweden and other countries and comment on the implications on the sustainability of pension systems. In particular, the Finnish life expectancy adjustment and the Swedish NDC system will be mentioned.

**9/2, Stas Volkov, University of Lund, Forest fires on integers**

Abstract:

Consider the following version of the forest-fire model on graph G. Each vertex of a graph becomes occupied with rate one. A fixed chosen vertex, say v, is hit by a lightning with the same rate, and then the whole cluster of occupied vertices containing v is completely burnt out. I will show that when G = Z+, the times between consecutive burnouts, properly scaled, converge weakly to a random variable which distribution is one minus the Dickman function.

Consider the following version of the forest-fire model on graph G. Each vertex of a graph becomes occupied with rate one. A fixed chosen vertex, say v, is hit by a lightning with the same rate, and then the whole cluster of occupied vertices containing v is completely burnt out. I will show that when G = Z+, the times between consecutive burnouts, properly scaled, converge weakly to a random variable which distribution is one minus the Dickman function.

Time permitting, I will also demonstrate that on transitive graphs with a non-trivial site percolation threshold and one infinite cluster at most, the distribution of the time until the first burnout of any single vertex has an exponential tail.

**16/2, Anton Muratov, Bit Flipping Models**

Abstract:

In many areas of engineering and science one faces with an array of devices which possess a few states. In the simplest case these could be on-off or idle-activated states, in other situations broken or `dead' states are added. If the activation-deactivation (flipping) or breakage cycles produce in a random fashion, a natural question to ask is when, if at all, the system of devices, which we call bits, recovers to some initial or ground state. By this we usually mean the state when all the bits are not active, allowing only for idling and/or broken bits to be seen. When the number of bits is infinite, the time to recover may assume infinite values when the system actually does not recover or finite values. In the former case we speak of transient behaviour of the system. In the latter case, depending of whether the mean of the recover time exists or not, we speak of positive or null-recurrence of the system. The terminology is borrowed from Markov chains setting and the above classification is tightly related to the exact random mechanism governing the change of bits' states.

In many areas of engineering and science one faces with an array of devices which possess a few states. In the simplest case these could be on-off or idle-activated states, in other situations broken or `dead' states are added. If the activation-deactivation (flipping) or breakage cycles produce in a random fashion, a natural question to ask is when, if at all, the system of devices, which we call bits, recovers to some initial or ground state. By this we usually mean the state when all the bits are not active, allowing only for idling and/or broken bits to be seen. When the number of bits is infinite, the time to recover may assume infinite values when the system actually does not recover or finite values. In the former case we speak of transient behaviour of the system. In the latter case, depending of whether the mean of the recover time exists or not, we speak of positive or null-recurrence of the system. The terminology is borrowed from Markov chains setting and the above classification is tightly related to the exact random mechanism governing the change of bits' states.

The main result for models involving infinite number of bits is the existence of the critical decay of flipping intensities, at which the model changes from transient to the recurrent behaviour. Besides, a central limit theorem can be established for the exact way system behaves in the transient regime.

**1/3, Oleg Sysoev, Linköping University, Monotonic regression for large multivariate datasets**

Short description: Monotonic regression is a non-parametric statistical method that is designed especially for applications in which the expected value of a response variable increases or decreases in one or more explanatory variables. Such applications can be found in business, physics, biology, medicine, signal processing, and other areas. In this talk, new algorithms, that make it feasible to fit monotonic functions to more than one hundred thousand data points, will be presented. It will be demonstrated that these algorithms offer high accuracy and, compared to traditional algorithms, represent considerable improvements with respect to computational time and memory requirements. Moreover, new methods for estimation of the uncertainty of a monotonic regression model will be suggested.

27/3, Tatyana Turova, Lunds University, Bootstrap percolation on some models of random graphs

27/3, Tatyana Turova, Lunds University, Bootstrap percolation on some models of random graphs

Abstract:

We shall first consider a bootstrap percolation on a classical homogeneous random graph. It is proved in a joint work with S. Janson, T. Luczak . and T. Vallier, that the phase transition is very sharp in this model. Then we discuss some modifications of the bootstrap process on inhomogeneous random graphs, related to the modelling of neuronal activity.

We shall first consider a bootstrap percolation on a classical homogeneous random graph. It is proved in a joint work with S. Janson, T. Luczak . and T. Vallier, that the phase transition is very sharp in this model. Then we discuss some modifications of the bootstrap process on inhomogeneous random graphs, related to the modelling of neuronal activity.

**17/4, Ronald Meester, Scaling limits in fractal percolation**

Abstract:

We use ideas from two-dimensional scaling limits to study curves in > the limiting set of the so called fractal percolation process. More precisely, we show that the set consisting of connected components larger than one point is a.s. the union of non-trivial Holder continuous curves, all with the same exponent. The interesting thing here is the relation between the almost sure convergence of the fractal to its limit set, seen as compact sets, and the weak convergence of curves in a different topology.

We use ideas from two-dimensional scaling limits to study curves in > the limiting set of the so called fractal percolation process. More precisely, we show that the set consisting of connected components larger than one point is a.s. the union of non-trivial Holder continuous curves, all with the same exponent. The interesting thing here is the relation between the almost sure convergence of the fractal to its limit set, seen as compact sets, and the weak convergence of curves in a different topology.

**24/4, Krzysztof Bartoszek and Serik Sagitov, Interspecies correlation for randomly evolving traits**

Abstract:

A simple way to model phenotypic evolution is to assume that after splitting, the trait values of the sister species diverge as independent Brownian motions or Ornstein-Uhlenbeck processes. Relying on a prior distribution for the underlying species tree (conditioned on the number of extant species) we study the vector of the observed trait values treating it a random sample of dependent observations. In this paper we derive compact formulae for the variance of the sample mean and the mean of the sample variance. The underlying species tree is modelled by a (supercritical or critical) conditioned branching process. In the critical case we modify the Aldous-Popovic model by assuming a proper prior for the time of origin.

A simple way to model phenotypic evolution is to assume that after splitting, the trait values of the sister species diverge as independent Brownian motions or Ornstein-Uhlenbeck processes. Relying on a prior distribution for the underlying species tree (conditioned on the number of extant species) we study the vector of the observed trait values treating it a random sample of dependent observations. In this paper we derive compact formulae for the variance of the sample mean and the mean of the sample variance. The underlying species tree is modelled by a (supercritical or critical) conditioned branching process. In the critical case we modify the Aldous-Popovic model by assuming a proper prior for the time of origin.

**8/5, Reinhard Bürger, Universität Wien, The effects of linkage and gene flow on local adaptation in a subdivided population: a deterministic two-locus model**

Abstract:

In spatially structured populations, gene flow may counteract local adaptation. We explore the combined effects of recombination and migration on the maintenance of genetic polymorphism and the degree of local adaptation in a spatially subdivided population. To this aim, we study a deterministic continent-island model of gene flow in which a derived (island) population experiences altered environmental conditions and receives maladaptive gene flow from the ancestral (continental) population. It is assumed that locally advantageous mutations have arisen on the island at two linked loci. Gene flow in concert with selection induces substantial linkage disequilibrium which substantially affects adaptation evolution and adaptation. The central mathematical result is an explicit characterization of all possible equilibrium configurations and bifurcation structures in the underlying two-locus model. From this, we deduce the dependence of the maximum amount of gene flow that admits the preservation of the locally adapted haplotype on the strength of recombination and selection. We also study the invasion of beneficial mutants of small effect that are linked to an already present, locally adapted allele. Because of linkage disequilibrium, mutants of much smaller effect can invade successfully than predicted by naive single-locus theory. This raises interesting questions on the evolution of the genetic architecture, in particular, about the emergence of clusters of tightly linked, slightly beneficial mutations and the evolution of recombination and chromosome inversions.

In spatially structured populations, gene flow may counteract local adaptation. We explore the combined effects of recombination and migration on the maintenance of genetic polymorphism and the degree of local adaptation in a spatially subdivided population. To this aim, we study a deterministic continent-island model of gene flow in which a derived (island) population experiences altered environmental conditions and receives maladaptive gene flow from the ancestral (continental) population. It is assumed that locally advantageous mutations have arisen on the island at two linked loci. Gene flow in concert with selection induces substantial linkage disequilibrium which substantially affects adaptation evolution and adaptation. The central mathematical result is an explicit characterization of all possible equilibrium configurations and bifurcation structures in the underlying two-locus model. From this, we deduce the dependence of the maximum amount of gene flow that admits the preservation of the locally adapted haplotype on the strength of recombination and selection. We also study the invasion of beneficial mutants of small effect that are linked to an already present, locally adapted allele. Because of linkage disequilibrium, mutants of much smaller effect can invade successfully than predicted by naive single-locus theory. This raises interesting questions on the evolution of the genetic architecture, in particular, about the emergence of clusters of tightly linked, slightly beneficial mutations and the evolution of recombination and chromosome inversions.

Literature: Bürger, R., and A. Akerman: The effects of linkage and gene flow on local adaptation: A two-locus continent-island model. Theoret. Popul. Biol. 80, 272-288 (2011)

**10/5, Reinhard Bürger, Universität Wien, Invasion and sojourn properties of locally beneficial mutations in a two-locus continent-island model of gene flow**

Abstract:

In subdivided populations, adaptation to a local environment may be hampered by maladaptive gene flow from other subpopulations. At an isolated locus, i.e., unlinked to other loci under selection, a locally beneficial mutation can be maintained only if its selective advantage exceeds the immigration rate of alternative allelic types. As explained in my other talk, recent deterministic theory in the context of a continent-island model shows that, if the beneficial mutation arises in linkage to a locus at which a locally adapted allele is already segregating in migration-selection balance, the new mutant can be maintained under much higher immigration rates than predicted by one-locus theory. This deterministic theory ignores stochastic effects which are especially important in the early phase during which the mutant is still rare. In this talk, I report about work in progress (jointly with Simon Aeschbacher) on a suite of stochastic models with the aim of quantifying the invasion and sojourn properties of mutants in one- and two-locus continent-island models. These models reach from multitype branching processes to diffusion processes and Markov chains of Wright-Fisher type. Preliminary analytical and numerical results will be presented that highlight the influence of the various sources of stochasticity.

In subdivided populations, adaptation to a local environment may be hampered by maladaptive gene flow from other subpopulations. At an isolated locus, i.e., unlinked to other loci under selection, a locally beneficial mutation can be maintained only if its selective advantage exceeds the immigration rate of alternative allelic types. As explained in my other talk, recent deterministic theory in the context of a continent-island model shows that, if the beneficial mutation arises in linkage to a locus at which a locally adapted allele is already segregating in migration-selection balance, the new mutant can be maintained under much higher immigration rates than predicted by one-locus theory. This deterministic theory ignores stochastic effects which are especially important in the early phase during which the mutant is still rare. In this talk, I report about work in progress (jointly with Simon Aeschbacher) on a suite of stochastic models with the aim of quantifying the invasion and sojourn properties of mutants in one- and two-locus continent-island models. These models reach from multitype branching processes to diffusion processes and Markov chains of Wright-Fisher type. Preliminary analytical and numerical results will be presented that highlight the influence of the various sources of stochasticity.

**15/5, Mari Myllymäki, Aalto University, Hierarchical modeling of second-order spatial structure of > epidermal nerve fiber patterns**

Abstract:

This talk discusses analysis of the second-order properties of the epidermal nerve fibers (ENFs) located in the epidermis, which is the outmost part of the skin. It has been observed that the ENF density decreases along diabetic neuropathy, while the spatial second-order analysis of ENFs has potential to detect and diagnose diabetic neuropathy in early stages when the ENF density may still be within the normal range. The data are suction skin blister samples from two body locations of healthy subjects and of subjects with diabetic neuropathy. The second-order property of the ENF entry points, i.e. the locations where the ENFs penetrate the epidermis, is summarized by a spatial summary function, namely Ripley's K function. We then apply a hierarchical latent Gaussian process regression in order to investigate how disease status and other covariates such as gender affect the level and shape of the second-order function, i.e. the degree of clustering of the points. This is work in progress.

This talk discusses analysis of the second-order properties of the epidermal nerve fibers (ENFs) located in the epidermis, which is the outmost part of the skin. It has been observed that the ENF density decreases along diabetic neuropathy, while the spatial second-order analysis of ENFs has potential to detect and diagnose diabetic neuropathy in early stages when the ENF density may still be within the normal range. The data are suction skin blister samples from two body locations of healthy subjects and of subjects with diabetic neuropathy. The second-order property of the ENF entry points, i.e. the locations where the ENFs penetrate the epidermis, is summarized by a spatial summary function, namely Ripley's K function. We then apply a hierarchical latent Gaussian process regression in order to investigate how disease status and other covariates such as gender affect the level and shape of the second-order function, i.e. the degree of clustering of the points. This is work in progress.

**22/5, Amandine Veber, Ecole Polytechnique, Paris, Evolution in a spatial continuum**

Abstract:

In this talk, we will present a general framework for studying the evolution of the genetic composition of a population scattered into some area of space. These models rely on a ’duality’ relation between the reproduction model and the corresponding genealogies of a sample, which is of great help in understanding the large scale behaviour of the local (or global) genetic diversities. Furthermore a great variety of scenarii can be described, ranging e.g. from very local reproduction events to very rare and massive extinction/recolonization events. In particular, we shall see how the parameters of local evolution can be inferred despite the (possible) presence of massive events in the distant past having a significant impact. (Joint work with N. Barton, A. Etheridge and J. Kelleher)

In this talk, we will present a general framework for studying the evolution of the genetic composition of a population scattered into some area of space. These models rely on a ’duality’ relation between the reproduction model and the corresponding genealogies of a sample, which is of great help in understanding the large scale behaviour of the local (or global) genetic diversities. Furthermore a great variety of scenarii can be described, ranging e.g. from very local reproduction events to very rare and massive extinction/recolonization events. In particular, we shall see how the parameters of local evolution can be inferred despite the (possible) presence of massive events in the distant past having a significant impact. (Joint work with N. Barton, A. Etheridge and J. Kelleher)

**24/5, Amandine Veber, Ecole Polytechnique, Paris, Large-scale behaviour of the spatial Lambda-Fleming-Viot process**

Abstract:

The SLFV process is a population model in which individuals live in a continuous space. Each of them also carries some heritable type or allele. We shall describe the long-term behaviour of this measure-valued process and that of the corresponding genealogical process of a sample of individuals in two cases : one that mimics the evolution of nearest-neighbour voter model (but in a spatial continuum), and one that allows some individuals to send offspring at very large distances. This is a joint work with Nathanaël Berestycki and Alison Etheridge.

The SLFV process is a population model in which individuals live in a continuous space. Each of them also carries some heritable type or allele. We shall describe the long-term behaviour of this measure-valued process and that of the corresponding genealogical process of a sample of individuals in two cases : one that mimics the evolution of nearest-neighbour voter model (but in a spatial continuum), and one that allows some individuals to send offspring at very large distances. This is a joint work with Nathanaël Berestycki and Alison Etheridge.

**31/5, Mattias Villani, Linköping University, Bayesian Methods for Flexible modeling of Conditional Distributions**

Abstract:

A general class of models and a unified Bayesian inference methodology is proposed for flexibly estimating the distribution of a continuous or discrete response variable conditional on a set of covariates. Our model is a finite mixture model with covariate-dependent mixing weights. The parameters in the mixture components are linked to sets of covariates, and special attention is given to the case where covariates enter the model nonlinearly through additive or surface splines. A new parametrization of the mixture and the use of an efficient MCMC algorithm with integrated Bayesian variable selection in all parts of the model successfully avoids over-fitting, even when the model is highly over-parameterized.

A general class of models and a unified Bayesian inference methodology is proposed for flexibly estimating the distribution of a continuous or discrete response variable conditional on a set of covariates. Our model is a finite mixture model with covariate-dependent mixing weights. The parameters in the mixture components are linked to sets of covariates, and special attention is given to the case where covariates enter the model nonlinearly through additive or surface splines. A new parametrization of the mixture and the use of an efficient MCMC algorithm with integrated Bayesian variable selection in all parts of the model successfully avoids over-fitting, even when the model is highly over-parameterized.

**7/6, Brunella Spinelli and Giacomo Zanella, Chalmers and University of Milan, Stable point processes: statistical inference and generalisations**

Abstract:

Stable point processes arise inevitably in various limiting schemes involving superposition of thinned point processes. When intensities of the processes are finite, the limit is Poisson, otherwise it is a discrete stable (DaS) point process with an infinite intensity measure and as such is an appealing model for various phenomena showing highly irregular (or bursty) behaviour. The first part of the talk will concentrate on estimation procedures of the distribution parameters of a stationary DaS process. The second part presents generalisations of the thinning procedure based on a branching process characterisations of the corresponding branching-stable processes. This generalisation is maximal in the sense that any operation replacing thinning which is required to possess natural associativity and distributivity with respect to superposition properties is necessarily a branching.

Stable point processes arise inevitably in various limiting schemes involving superposition of thinned point processes. When intensities of the processes are finite, the limit is Poisson, otherwise it is a discrete stable (DaS) point process with an infinite intensity measure and as such is an appealing model for various phenomena showing highly irregular (or bursty) behaviour. The first part of the talk will concentrate on estimation procedures of the distribution parameters of a stationary DaS process. The second part presents generalisations of the thinning procedure based on a branching process characterisations of the corresponding branching-stable processes. This generalisation is maximal in the sense that any operation replacing thinning which is required to possess natural associativity and distributivity with respect to superposition properties is necessarily a branching.

**4/9, Giacomo Zanella, Warwick University, UK: Branching stable point processes**

Abstract:

Branching stability is a recent concept in point processes and describe the limiting regime in superposition of point processes where particles are allowed to evolve independently according to a subcritical branching process. It is a far-reaching generalisation of the F-stability for non-negative integer random variables introduced in 2004 by Steutel and Van Harn. We fully characterise such processes in terms of their generating functionals and give their cluster representation for the case of non-migrating particles which correspond to Steutel and Van Harn case. We then extend our results to particular important examples of migration mechanism of the particles and characterise the corresponding stability. Branching stable point processes are believed to be an adequate model for contemporary telecommunications systems which show spatial burstiness, like the position of mobile telephones during festival activities in a big city.

Branching stability is a recent concept in point processes and describe the limiting regime in superposition of point processes where particles are allowed to evolve independently according to a subcritical branching process. It is a far-reaching generalisation of the F-stability for non-negative integer random variables introduced in 2004 by Steutel and Van Harn. We fully characterise such processes in terms of their generating functionals and give their cluster representation for the case of non-migrating particles which correspond to Steutel and Van Harn case. We then extend our results to particular important examples of migration mechanism of the particles and characterise the corresponding stability. Branching stable point processes are believed to be an adequate model for contemporary telecommunications systems which show spatial burstiness, like the position of mobile telephones during festival activities in a big city.

**6/9, Ilya Molchanov, University of Bern, Switzerland**

Abstract:

Invariance properties of random vectors and stochastic processes based on the zonoid concept Abstract: Two integrable random vectors in the Euclidean space are said to be zonoid equivalent if their projections on each given direction share the same first absolute moments. The paper analyses stochastic processes whose finite-dimensional distributions remain zonoid equivalent with respect to time shifts (zonoid stationarity) and permutations of time instances (swap-invariance). While the first concept is weaker than the stationarity, the second one is a weakening of the exchangeability property. It is shown that nonetheless the ergodic theorem holds for swap-invariant sequences.

Invariance properties of random vectors and stochastic processes based on the zonoid concept Abstract: Two integrable random vectors in the Euclidean space are said to be zonoid equivalent if their projections on each given direction share the same first absolute moments. The paper analyses stochastic processes whose finite-dimensional distributions remain zonoid equivalent with respect to time shifts (zonoid stationarity) and permutations of time instances (swap-invariance). While the first concept is weaker than the stationarity, the second one is a weakening of the exchangeability property. It is shown that nonetheless the ergodic theorem holds for swap-invariant sequences.

**25/9, Prof. Günter Last, Karlsruhe Institute of Technology, Germany: Fock space analysis of Poisson functionals - 1 & 2**

Abstract:

These are the first two lectures in the series of four-lecture course summarising some recent developments in the theory of general Poisson processes. It can also be passed as a PhD course "Poisson measures" organised by Prof. Sergei Zuyev. His introductory lectures on the field are held on Tuesday 18/09 13:15-15:00 and Thursday 20/09 13:15-15:00. In the first lecture we will prove an explicit Fock space representation of square-integrable functions of a general Poisson process based on iterated difference operators [1]. As general applications we shall discuss explicit Wiener-Ito chaos expansions and some basic properties of Malliavin operators [1]. In the second lecture we will derive covariance identities and the Clark-Okone martingale representation for Poisson martingales [2]. Our first application are short proofs of the Poincare- and the FKG-inequality for Poisson processes. A second application is Wu's [3] elegant proof of a general log-Sobolev inequality for Poisson processes. The final application is minimal variance hedging for financial markets driven by Levy processes.

These are the first two lectures in the series of four-lecture course summarising some recent developments in the theory of general Poisson processes. It can also be passed as a PhD course "Poisson measures" organised by Prof. Sergei Zuyev. His introductory lectures on the field are held on Tuesday 18/09 13:15-15:00 and Thursday 20/09 13:15-15:00. In the first lecture we will prove an explicit Fock space representation of square-integrable functions of a general Poisson process based on iterated difference operators [1]. As general applications we shall discuss explicit Wiener-Ito chaos expansions and some basic properties of Malliavin operators [1]. In the second lecture we will derive covariance identities and the Clark-Okone martingale representation for Poisson martingales [2]. Our first application are short proofs of the Poincare- and the FKG-inequality for Poisson processes. A second application is Wu's [3] elegant proof of a general log-Sobolev inequality for Poisson processes. The final application is minimal variance hedging for financial markets driven by Levy processes.

References:

[1] Last, G. and Penrose, M.D. (2011). Fock space representation, chaos expansion and covariance inequalities for general Poisson processes. Probability Theory Related Fields, 150, 663-690.

[2] Last, G. and Penrose, M.D. (2011). Martingale representation for Poisson processes with applications to minimal variance hedging. Stochastic Processes and their Applications 121, 1588-1606.

[3] Wu, L. (2000). A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probability Theory Related Fields 118, 427-438.

[1] Last, G. and Penrose, M.D. (2011). Fock space representation, chaos expansion and covariance inequalities for general Poisson processes. Probability Theory Related Fields, 150, 663-690.

[2] Last, G. and Penrose, M.D. (2011). Martingale representation for Poisson processes with applications to minimal variance hedging. Stochastic Processes and their Applications 121, 1588-1606.

[3] Wu, L. (2000). A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probability Theory Related Fields 118, 427-438.

**27/9, Prof. Günter Last, Karlsruhe Institute of Technology, Germany: Fock space analysis of Poisson functionals - 3 & 4**

Abstract:

These are the last two lectures in the series of four-lecture course summarising some recent developments in the theory of general Poisson processes. It can also be passed as a PhD course "Poisson measures" organised by Prof. Sergei Zuyev. His introductory lectures on the field are held on Tuesday 18/09 13:15-15:00 and Thursday 20/09 13:15-15:00. The third lecture presents some general theory for the perturbation analysis of Poisson processes [1] together with an application to multivariate Levy processes. The fourth and final lecture discusses the recent central limit theorem from [4] that is based on a nice combination of Malliavin calculus and the Stein-Chen method. We will apply this result as well as those from [2] to Poisson flat processes from stochastic geometry [3].

These are the last two lectures in the series of four-lecture course summarising some recent developments in the theory of general Poisson processes. It can also be passed as a PhD course "Poisson measures" organised by Prof. Sergei Zuyev. His introductory lectures on the field are held on Tuesday 18/09 13:15-15:00 and Thursday 20/09 13:15-15:00. The third lecture presents some general theory for the perturbation analysis of Poisson processes [1] together with an application to multivariate Levy processes. The fourth and final lecture discusses the recent central limit theorem from [4] that is based on a nice combination of Malliavin calculus and the Stein-Chen method. We will apply this result as well as those from [2] to Poisson flat processes from stochastic geometry [3].

References:

[1] Last, G. (2012). Perturbation analysis of Poisson processes. arXiv:1203.3181v1.

[2] Last, G. and Penrose, M.D. (2011). Fock space representation, chaos expansion and covariance inequalities for general Poisson processes. Probability Theory Related Fields, 150, 663-690.

[3] Last, G., Penrose, M.D., Schulte, M. and Th"ale, C. (2012). Moments and central limit theorems for some multivariate Poisson functionals. arXiv: 1205.3033v1.

[4] Peccati, G., Sole, J.L., Taqqu, M.S. and Utzet, F. (2010). Stein's method and normal approximation of Poisson functionals. Annual Probability 38, 443-478.

[1] Last, G. (2012). Perturbation analysis of Poisson processes. arXiv:1203.3181v1.

[2] Last, G. and Penrose, M.D. (2011). Fock space representation, chaos expansion and covariance inequalities for general Poisson processes. Probability Theory Related Fields, 150, 663-690.

[3] Last, G., Penrose, M.D., Schulte, M. and Th"ale, C. (2012). Moments and central limit theorems for some multivariate Poisson functionals. arXiv: 1205.3033v1.

[4] Peccati, G., Sole, J.L., Taqqu, M.S. and Utzet, F. (2010). Stein's method and normal approximation of Poisson functionals. Annual Probability 38, 443-478.

**28/9, Martin Rosvall, Umeå universitet: Mapping change in large networks**

Abstract:

Change is a fundamental ingredient of interaction patterns in biology, technology, the economy, and science itself: Interactions within and between organisms change; transportation patterns by air, land, and sea all change; the global financial flow changes; and the frontiers of scientific research change. Networks and clustering methods have become important tools to comprehend instances of these large-scale structures, but without methods to distinguish between real trends and noisy data, these approaches are not useful for studying how networks change. Only if we can assign significance to the partitioning of single networks can we distinguish meaningful structural changes from random fluctuations. Here we show that bootstrap resampling accompanied by significance clustering provides a solution to this problem. To connect changing structures with the changing function of networks, we highlight and summarize the significant structural changes with alluvial diagrams and realize de Solla Price's vision of mapping change in science: studying the citation pattern between about 7000 scientific journals over the past decade, we find that neuroscience has transformed from an interdisciplinary specialty to a mature and stand-alone discipline.

Change is a fundamental ingredient of interaction patterns in biology, technology, the economy, and science itself: Interactions within and between organisms change; transportation patterns by air, land, and sea all change; the global financial flow changes; and the frontiers of scientific research change. Networks and clustering methods have become important tools to comprehend instances of these large-scale structures, but without methods to distinguish between real trends and noisy data, these approaches are not useful for studying how networks change. Only if we can assign significance to the partitioning of single networks can we distinguish meaningful structural changes from random fluctuations. Here we show that bootstrap resampling accompanied by significance clustering provides a solution to this problem. To connect changing structures with the changing function of networks, we highlight and summarize the significant structural changes with alluvial diagrams and realize de Solla Price's vision of mapping change in science: studying the citation pattern between about 7000 scientific journals over the past decade, we find that neuroscience has transformed from an interdisciplinary specialty to a mature and stand-alone discipline.

**11/10, Nanny Wermuth, Chalmers and International Agency of Research on Cancer, Lyon, France**

Abstract:

Traceable regressions applied to the Mannhein study of children at risk Abstract: We define and study the concept of traceable regressions and apply it to some examples. Traceable regressions are sequences of conditional distributions in joint or single responses for which a corresponding graph captures an independence structure and represents, in addition, conditional dependences that permit the tracing of pathways of dependence. We give the properties needed for transforming these graphs and graphical criteria to decide whether a path in the graph induces a dependence. The much stronger constraints on distributions that are faithful to a graph are compared to those needed for traceable regressions.

Traceable regressions applied to the Mannhein study of children at risk Abstract: We define and study the concept of traceable regressions and apply it to some examples. Traceable regressions are sequences of conditional distributions in joint or single responses for which a corresponding graph captures an independence structure and represents, in addition, conditional dependences that permit the tracing of pathways of dependence. We give the properties needed for transforming these graphs and graphical criteria to decide whether a path in the graph induces a dependence. The much stronger constraints on distributions that are faithful to a graph are compared to those needed for traceable regressions.

**18/10, Stas Volkov, Lund University: On random geometric subdivisions**

Abstract:

I will present several models of random geometric subdivisions, similar to that of Diaconis and Miclo (Combinatorics, Probability and Computing, 2011), where a triangle is split into 6 smaller triangles by its medians, and one of these parts is randomly selected as a new triangle, and the process continues ad infinitum. I will show that in a similar model the limiting shape of an indefinite subdivision of a quadrilateral is a parallelogram. I will also show that the geometric subdivisions of a triangle by angle bisectors converge (but only weakly) to a non-atomic distribution, and, time permitting, that the geometric subdivisions of a triangle by choosing a uniform random points on its sides converges to a “flat” triangle, similarly to the result of the paper mentioned above.

I will present several models of random geometric subdivisions, similar to that of Diaconis and Miclo (Combinatorics, Probability and Computing, 2011), where a triangle is split into 6 smaller triangles by its medians, and one of these parts is randomly selected as a new triangle, and the process continues ad infinitum. I will show that in a similar model the limiting shape of an indefinite subdivision of a quadrilateral is a parallelogram. I will also show that the geometric subdivisions of a triangle by angle bisectors converge (but only weakly) to a non-atomic distribution, and, time permitting, that the geometric subdivisions of a triangle by choosing a uniform random points on its sides converges to a “flat” triangle, similarly to the result of the paper mentioned above.

**1/11, Uwe Rösler, University of Kiel: On Stochastic Fixed Point Equations and the Weighted Branching Process**

Abstract:

Stochastic fixed point equations X=f(U,(X_n)_{n\in\N}) U, X_i are independent and X_i=X (all equalities are in distribution) have now some interest of its own. The starting point was the characterization of the limiting distribution of the sorting QUICKSORT as a solution of a fixed point equation. After that many more examples popped up, characterization of old ones like stable distributions, many new ones in the analysis of algorithms by the contraction method, in population dynamics and in financial mathematics.

Stochastic fixed point equations X=f(U,(X_n)_{n\in\N}) U, X_i are independent and X_i=X (all equalities are in distribution) have now some interest of its own. The starting point was the characterization of the limiting distribution of the sorting QUICKSORT as a solution of a fixed point equation. After that many more examples popped up, characterization of old ones like stable distributions, many new ones in the analysis of algorithms by the contraction method, in population dynamics and in financial mathematics.

They appear whenever we face a stochastic process involving some branching. The classical easiest example are branching processes with the limit of the intrinsic martingale Z_n/m^n. While the theory of branching processes is pretty analytic using generating functions, for the generalization, the Weighted Branching Processes as a tree indexed stochastic process, probabilistic methods and interpretation appear again and many new probabilistic methods were developed, e.g. the contraction method.

**8/11, Eugene Mamontov, Chalmers: Non-stationary invariant and dynamic-equilibrium Markov stochastic processes**

Abstract:

The present work considers continuous Markov stochastic processes defined in the entire time axis. They are of a considerable importance in the natural/life sciences and engineering. They draw attention to invariant Markov processes, which are non-stationary. The work discusses the key features of latter processes, their covariance and spectral-density functions, as well as some of the related notions such as dynamic equilibrium Markov processes and stability in distribution. The meaning of the dynamic equilibrium processes is also emphasized in connection with their role in living systems.

The present work considers continuous Markov stochastic processes defined in the entire time axis. They are of a considerable importance in the natural/life sciences and engineering. They draw attention to invariant Markov processes, which are non-stationary. The work discusses the key features of latter processes, their covariance and spectral-density functions, as well as some of the related notions such as dynamic equilibrium Markov processes and stability in distribution. The meaning of the dynamic equilibrium processes is also emphasized in connection with their role in living systems.

**13/11, Måns Henningson, Chalmers: Quantum theory and probability**

Abstract:

Classical physics fall in the framework of philosophical realism: There are objective facts, regardless of our knowledge about them. Einstein added that each such fact must be localized in space-time, and that its influence could not propagate faster than the speed of light. The result of an experiment is in principle determined by these facts, but possibly there are also "hidden variables" whose values we cannot directly determine. One could then introduce a probability distribution for these, from which follows a probability distribution for the result of our experiment. Quantum physics gives a rather different view of the world. Here "randomness" appears to enter at a more fundamental level and has nothing to do with our lack of knowledge of any hidden variables. John Bell constructed a Gedankenexperiment (which has later been performed in reality) to shed light on this. He derived, under the assumptions of classical physics together with Einstein's amendment, an inequality that must be obeyed by certain statistical correlations for experimental results. Quantum physics violates the Bell inequalities, and the real experiments confirm quantum physics. This conflict in a sense derives from the quantum notion of "entanglement", which does not have any classical counterpart: It reflects the impossibility to describe the state of a composite system in terms of the states of its constituent parts (which do not even have to "interact" with each other).

Classical physics fall in the framework of philosophical realism: There are objective facts, regardless of our knowledge about them. Einstein added that each such fact must be localized in space-time, and that its influence could not propagate faster than the speed of light. The result of an experiment is in principle determined by these facts, but possibly there are also "hidden variables" whose values we cannot directly determine. One could then introduce a probability distribution for these, from which follows a probability distribution for the result of our experiment. Quantum physics gives a rather different view of the world. Here "randomness" appears to enter at a more fundamental level and has nothing to do with our lack of knowledge of any hidden variables. John Bell constructed a Gedankenexperiment (which has later been performed in reality) to shed light on this. He derived, under the assumptions of classical physics together with Einstein's amendment, an inequality that must be obeyed by certain statistical correlations for experimental results. Quantum physics violates the Bell inequalities, and the real experiments confirm quantum physics. This conflict in a sense derives from the quantum notion of "entanglement", which does not have any classical counterpart: It reflects the impossibility to describe the state of a composite system in terms of the states of its constituent parts (which do not even have to "interact" with each other).

**15/11, Anders Johansson, Gävle: Existence of matchings in random sub-hypergraphs**

Abstract: I will discuss the matching problem of hypergraphs and some generalisations. The context is that of determining asymptotic zero-one laws for the existence of a matching in a random sub-hypergraph

*H*of a fixed hypergraph*G*. Such laws can be established when, say,*G*is complete and*H*is a Bernoulli process on*G*, using a local symmetry of the distribution of*H*. The same symmetry argument allows for the problem of fi nding factors in random graphs. I will also discuss problems regarding Latin Squares where this argument breaks down and where new ideas are needed.**22/11, David Bolin, University of Lund: Excursion and contour uncertainty regions for latent Gaussian models**

Abstract:

An interesting statistical problem is to find regions where some studied process exceeds a certain level. Estimating these regions so that the probability for exceeding the level jointly in the entire set is some predefined value is a difficult problem that occurs in several areas of applications ranging from brain imaging to astrophysics. In this work, we propose a method for solving this problem, and the related problem of finding uncertainty regions for contour curves, for latent Gaussian models. The method is based on using a parametric family for the excursion sets in combination with integrated nested Laplace approximations and an importance sampling-based algorithm for estimating joint probabilities. The accuracy of the method is investigated using simulated data and two environmental applications are presented. In the first, areas where the air pollution in the Piemonte region in northern Italy exceeds the daily limit value, set by the European Union for human health protection, are estimated. In the second, regions in the African Sahel that experienced an increase in vegetation after the drought period in the early 1980s are estimated.

An interesting statistical problem is to find regions where some studied process exceeds a certain level. Estimating these regions so that the probability for exceeding the level jointly in the entire set is some predefined value is a difficult problem that occurs in several areas of applications ranging from brain imaging to astrophysics. In this work, we propose a method for solving this problem, and the related problem of finding uncertainty regions for contour curves, for latent Gaussian models. The method is based on using a parametric family for the excursion sets in combination with integrated nested Laplace approximations and an importance sampling-based algorithm for estimating joint probabilities. The accuracy of the method is investigated using simulated data and two environmental applications are presented. In the first, areas where the air pollution in the Piemonte region in northern Italy exceeds the daily limit value, set by the European Union for human health protection, are estimated. In the second, regions in the African Sahel that experienced an increase in vegetation after the drought period in the early 1980s are estimated.

**29/11, Dietrich von Rosen, SLU Uppsala: From univariate linear to multilinear models**

Abstract:

The presentation is based on a number of figures illustrating appropriate linear spaces reflecting a tour from univariate to multilinear models. The start is the classical Gauss-Markov model from where we jump into the multivariate world, i.e. MANOVA. The next stop will be the Growth Curve model and then a quick exposure of Extended growth curves will take place. The tour is ended with some comments on multilinear models

The presentation is based on a number of figures illustrating appropriate linear spaces reflecting a tour from univariate to multilinear models. The start is the classical Gauss-Markov model from where we jump into the multivariate world, i.e. MANOVA. The next stop will be the Growth Curve model and then a quick exposure of Extended growth curves will take place. The tour is ended with some comments on multilinear models

**11/12, Jimmy Olsson,**

**Lund University:**Metropolising forward particle filtering backward simulation and Rao-Blackwellisation using multiple trajectoriesAbstract:

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distribution. In recent years there has been an increased interest in Monte Carlo-based methods, often involving particle filters, for approximate smoothing in nonlinear and/or non-Gaussian state-space models. One such method is to approximate filter distributions using a particle filter and then to simulate, using backward kernels, a state trajectory backwards on the set of particles. In this talk we show that by simulating multiple realizations of the particle filter and adding a Metropolis-Hastings step, one obtains a Markov chain Monte Carlo scheme whose stationary distribution is the exact smoothing distribution. This procedure expands upon a similar one recently proposed by Andrieu, Doucet, Holenstein, and Whiteley. We also show that simulating multiple trajectories from each realization of the particle filter can be beneficial from a perspective of variance versus computation time, and illustrate this idea using two examples.

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distribution. In recent years there has been an increased interest in Monte Carlo-based methods, often involving particle filters, for approximate smoothing in nonlinear and/or non-Gaussian state-space models. One such method is to approximate filter distributions using a particle filter and then to simulate, using backward kernels, a state trajectory backwards on the set of particles. In this talk we show that by simulating multiple realizations of the particle filter and adding a Metropolis-Hastings step, one obtains a Markov chain Monte Carlo scheme whose stationary distribution is the exact smoothing distribution. This procedure expands upon a similar one recently proposed by Andrieu, Doucet, Holenstein, and Whiteley. We also show that simulating multiple trajectories from each realization of the particle filter can be beneficial from a perspective of variance versus computation time, and illustrate this idea using two examples.

**13/12, Erik Lindström, Lund University: Tuned Iterated Filtering**

Abstract:

Maximum Likelihood estimation for partially observed Markov process models is a non-trivial problem, as the likelihood function often is unknown. Iterated Filtering is a simple, yet very general algorithm for computing the Maximum Likelihood estimate. The algorithm is 'plug and play' in the sense that it can be used with rudimentary statistical knowledge. The purpose of this talk is to discuss the algorithm, pointing out practical limitations, and suggest extensions and/or modifications that will improve the robustness and/or performance of the algorithm. We will also discuss the connection between the Iterated Filtering algorithm, and algorithms commonly used in engineering (system identification, signal processing etc.), illustrating that a similar algorithm has been known for several decades.

Maximum Likelihood estimation for partially observed Markov process models is a non-trivial problem, as the likelihood function often is unknown. Iterated Filtering is a simple, yet very general algorithm for computing the Maximum Likelihood estimate. The algorithm is 'plug and play' in the sense that it can be used with rudimentary statistical knowledge. The purpose of this talk is to discuss the algorithm, pointing out practical limitations, and suggest extensions and/or modifications that will improve the robustness and/or performance of the algorithm. We will also discuss the connection between the Iterated Filtering algorithm, and algorithms commonly used in engineering (system identification, signal processing etc.), illustrating that a similar algorithm has been known for several decades.

## 2011

**13/1 Dr. Raphaël Lachièze-Rey, University of Lille-1, France: Ergodicity of STIT tessellations**

Abstract:

Random tessellations form a relevant class of models for many natural phenomena in biology, geology, materials science. STIT tessellations (for STable under ITeration), introduced in the 2000's, are characterised by their stability under an operation called "iteration", which confers to them a privileged role in modelling phenomena of cracking or of division in nature. After a clear exposition of the model, we will present its main characteristics, establishing in particular its mixing properties.

Random tessellations form a relevant class of models for many natural phenomena in biology, geology, materials science. STIT tessellations (for STable under ITeration), introduced in the 2000's, are characterised by their stability under an operation called "iteration", which confers to them a privileged role in modelling phenomena of cracking or of division in nature. After a clear exposition of the model, we will present its main characteristics, establishing in particular its mixing properties.

**27/1 Alexey Lindo, Department of Mathematical Sciences, Chalmers University of Technology: A probabilistic analysis of Wagner's k-tree algorithm**

Abstract:

David Wagner introduced an algorithm for solving a k-dimensional generalization of the birthday problem (see [1]). It has wide applications in cryptography and cryptanalysis. A probabilistic model of Wagner's algorithm can be described as follows. Suppose that elements of the input lists are drawn from additive group of integers modulo $n$. Let the random variable W represents the number of solutions found by Wagner's algorithm in the introduced model. We first observe that W is the sum of the dependent indicators. Then using Chen-Stein method we derive Poisson approximation to the distribution of W. An upper bound on a total variation distance given in [2,3] is particularly essential for the proof. The bound allows to estimate the strength of encoding by the algorithm in terms of its parameters.

David Wagner introduced an algorithm for solving a k-dimensional generalization of the birthday problem (see [1]). It has wide applications in cryptography and cryptanalysis. A probabilistic model of Wagner's algorithm can be described as follows. Suppose that elements of the input lists are drawn from additive group of integers modulo $n$. Let the random variable W represents the number of solutions found by Wagner's algorithm in the introduced model. We first observe that W is the sum of the dependent indicators. Then using Chen-Stein method we derive Poisson approximation to the distribution of W. An upper bound on a total variation distance given in [2,3] is particularly essential for the proof. The bound allows to estimate the strength of encoding by the algorithm in terms of its parameters.

[1] D. Wagner. A generalized birthday problem. http://www.cs.berkeley.edu/~daw/papers/genbday.html

[2] R. Arratia, L. Goldstein and L. Gordon. Two Moments Suffice for Poisson Approximations: The Chen-Stein Method.

[3] L.H.Y. Chen. Poisson approximation for dependent trials.

**3/2 Sergei Zuyev, Chalmers: Discussion seminar - Optimal design of dilution experiments**

Abstract:

This is the first in a (hopefully) series of Discussion seminars: more questions than answers are expected, so come open-minded and be ready for discussion!

This is the first in a (hopefully) series of Discussion seminars: more questions than answers are expected, so come open-minded and be ready for discussion!

Stem cells generated a lot of excitement in the last decade: these are cells produced in an embryo and they have capability to turn into specialised tissue cells which potentially opens a way to cure many diseases. In recent stem-cells research the following experiment was conducted. Haematopoietic stem cells (HSC) were extracted from a mouse embryo and then transplanted into adult recipient mice which previously received a doze of potentially deadly radiation doze. After such treatment, all the mice recovered successfully.

The problem, however, is to estimate how many HSCs were extracted from the embryo if we know that even one such cell is sufficient for a mouse to recover? Unfortunately, there is still no way to count this number directly, say, by using a microscope. The answer can be obtained by carefully designing experiment when a differently diluted dozes are transplanted to different irradiated mice, so that inevitably some of the mice do not receive any HSCs. Then the proportion of survived mice as a function of the dilution rate allows to estimate the number of HSC extracted. The main constraint in designing such experiment is that we want to save as much lab mice as possible, but still get sensible quality estimates.

**17/2 Peter Gennemark, Mathematical sciences: Identifying and compensating for systematic errors in a large-scale phenotypic screens**

Abstract:

We consider statistical questions concerning analysis of yeast growth curves. Each curve is based on measurements of the growth of a cell culture during 48 hours with three measurements per hour. The experimental set-up is large scale and allows 200 cultures to be monitored simultaneously. We study reproducibility in such large-scale experiments using a set of control experiments of only wild-type strains.

We consider statistical questions concerning analysis of yeast growth curves. Each curve is based on measurements of the growth of a cell culture during 48 hours with three measurements per hour. The experimental set-up is large scale and allows 200 cultures to be monitored simultaneously. We study reproducibility in such large-scale experiments using a set of control experiments of only wild-type strains.

It is found that the false-positive rate is under-estimated in current significance tests, partly because of bias from, e.g., spatial plate effects, that affect the tests when high precision measurement techniques are used, and partly because of dependence between repetitions in the current design. By stringent data pre-processing and improved experimental design it is demonstrated that one can counter the effects of systematic errors and increase the accuracy.

Joint work with Olle Nerman (Mathematical sciences) and Anders Blomberg (Cell and Molecular Biology, GU)

**24/2 Takis Konstantopoulos, Uppsala University: A stochastic ordered graph model**

Abstract:

We consider a stochastic directed graph on the integers whereby a directed edge between $i$ and a larger integer $j$ exists with probability $p_{j-i}$ depending solely on the distance between the two integers. Under broad conditions, we identify a regenerative structure that enables us to prove limit theorems for the maximal path length in a long chunk of the graph. We first discuss background literature of this stochastic model. The model is an extension of a special case of graphs studied by Foss and the speaker. We then consider a similar type of graph but on the `slab' $\Z \times I$, where $I$ is a finite partially ordered set. We extend the techniques introduced in the in the first part of the paper to obtain a central limit theorem for the longest path. When $I$ is linearly ordered, the limiting distribution can be seen to be that of the largest eigenvalue of a $|I| \times |I|$ random matrix in the Gaussian unitary ensemble (GUE). This is joint work with S Foss and D Denisov.

We consider a stochastic directed graph on the integers whereby a directed edge between $i$ and a larger integer $j$ exists with probability $p_{j-i}$ depending solely on the distance between the two integers. Under broad conditions, we identify a regenerative structure that enables us to prove limit theorems for the maximal path length in a long chunk of the graph. We first discuss background literature of this stochastic model. The model is an extension of a special case of graphs studied by Foss and the speaker. We then consider a similar type of graph but on the `slab' $\Z \times I$, where $I$ is a finite partially ordered set. We extend the techniques introduced in the in the first part of the paper to obtain a central limit theorem for the longest path. When $I$ is linearly ordered, the limiting distribution can be seen to be that of the largest eigenvalue of a $|I| \times |I|$ random matrix in the Gaussian unitary ensemble (GUE). This is joint work with S Foss and D Denisov.

**3/3 Victor Brovkin, Max Planck Institute for Meteorology, Hamburg, Germany: Land biosphere models for future climate projections**

Abstract:

The Earth System Models (ESMs) are the best tools available for projecting changes in the atmospheric CO2 concentration and climate in the coming decades and centuries. ESMs include models of land biosphere which are based on well established understanding of plant physiology and ecology, but these models typically use very few observations to constrain model parameters. Extensive ground-based measurements of plant biochemistry, physiology, and ecology have led to a much better quantification of ecosystem processes during the last decades. Recent assimilation of many thousands of measurements of species traits in global databases opens a new perspective to specify plant parameters used in ecosystem models which predominantly operate at the level of large-scale plant units such as plant functional types (PFTs). Instead of constraining model parameters using values from a few publications, a novel approach aggregates plant traits from the species level to the PFT level using trait databases. A study to employ two global databases linking plant functional types to decomposition rates of wood and leaf litter to improve future projections of climate and carbon cycle using an intermediate complexity ESM, CLIMBER-LPJ, will be presented.

The Earth System Models (ESMs) are the best tools available for projecting changes in the atmospheric CO2 concentration and climate in the coming decades and centuries. ESMs include models of land biosphere which are based on well established understanding of plant physiology and ecology, but these models typically use very few observations to constrain model parameters. Extensive ground-based measurements of plant biochemistry, physiology, and ecology have led to a much better quantification of ecosystem processes during the last decades. Recent assimilation of many thousands of measurements of species traits in global databases opens a new perspective to specify plant parameters used in ecosystem models which predominantly operate at the level of large-scale plant units such as plant functional types (PFTs). Instead of constraining model parameters using values from a few publications, a novel approach aggregates plant traits from the species level to the PFT level using trait databases. A study to employ two global databases linking plant functional types to decomposition rates of wood and leaf litter to improve future projections of climate and carbon cycle using an intermediate complexity ESM, CLIMBER-LPJ, will be presented.

**10/3 Andrey Lange, Bauman Moscow State Technical University: Discrete stochastic systems with pairwise interaction**

Abstract:

A model of a system of interacting particles of types T_1, ... , T_n is considered as a continuous-time Markov process on a countable state space. Forward and backward Kolmogorov systems of differential equations are represented in a form of partial differential equations for the generating functions of transition probabilities. We study the limiting behaviour of probability distributions as time tends to infinity for two models of that type.

A model of a system of interacting particles of types T_1, ... , T_n is considered as a continuous-time Markov process on a countable state space. Forward and backward Kolmogorov systems of differential equations are represented in a form of partial differential equations for the generating functions of transition probabilities. We study the limiting behaviour of probability distributions as time tends to infinity for two models of that type.

First model deals with an open system with pairwise interaction. New particles T immigrate either one or two particles at a time, and the interaction T+T leads to the death of either one or both of the interacting particles. The distribution of the number of particles is studied as the time tends to infinity. The exact solutions of the stationary Kolmogorov equations were found in terms of Bessel and hypergeometric functions. The asymptotics for the expectation and variance as well as the asymptotic normality of the stationary distribution were obtained when the intensity of new particles arrival is high.

The second model describes a system with particles T1 and T2. Particles of the two types appear either as the offspring of a particle of type T1 or as a result of interaction T1+T1. The distribution of the final number of particles T2 is considered when the subpopulation of particles T1 becomes extinct. Under certain restrictions on the distribution of the number of appearing particles, the asymptotics for the expectation and variance as well as the asymptotic normality of the final distribution are obtained when the initial number of particles T1 is large.

**10/3, Graham Jones, Durness, Scotland: Stochastic models for phylogenetic trees and networks**

Abstract:

The Tree of Life does not look as though it was generated by a constant rate birth-death process, since too many nodes show unbalanced splits where one branch leads to only a few tips and the other to very many. Generalizations of the constant rate birth-death process (age-dependent and multitype binary branching processes) can produce trees which look more like real phylogenetic trees. A method for numerical calculation of the probability distributions of these trees will be presented.

The Tree of Life does not look as though it was generated by a constant rate birth-death process, since too many nodes show unbalanced splits where one branch leads to only a few tips and the other to very many. Generalizations of the constant rate birth-death process (age-dependent and multitype binary branching processes) can produce trees which look more like real phylogenetic trees. A method for numerical calculation of the probability distributions of these trees will be presented.

Hybridization produces phylogenetic networks instead of trees, and things can get complicated even in the simplest cases. What sequences of evolutionary events (speciations, extinctions and hybridizations) can produce two diploids and one tetraploid from a single diploid ancestor?

**31/3, Stig Larsson: Numerical approximation of stochastic PDEs**

Abstract:

Together with several co-workers during recent years I have studied numerical approximation of evolution PDEs perturbed by noise. You may consider this as a ''discussion seminar'' where I will review our work and ask for your advice and possible cooperation for future work.

Together with several co-workers during recent years I have studied numerical approximation of evolution PDEs perturbed by noise. You may consider this as a ''discussion seminar'' where I will review our work and ask for your advice and possible cooperation for future work.

**9/4, Dustin Cartwright, Berkeley: How are SNPs distributed in genes?**

Abstract:

The organization of genes into 3-base codons has certain consequences for the distribution of bases. Many of these consequences have been known for a long time. I will talk about a particular method for detecting these artefacts if we didn't already know the underlying cause. The central analytical tool will be the notion of the rank of a tensor.

The organization of genes into 3-base codons has certain consequences for the distribution of bases. Many of these consequences have been known for a long time. I will talk about a particular method for detecting these artefacts if we didn't already know the underlying cause. The central analytical tool will be the notion of the rank of a tensor.

**3/5, Maria Deijfen, Stockholm University: Scale-free percolation**

Abstract:

I will describe a model for inhomogeneous long-range percolation on Z^d with potential applications in network modeling. Each vertex is independently assigned a non-negative random weight and the probability that there is an edge between two given vertices is then determined by a certain function of their weights and of the distance between them. The results concern the degree distribution in the resulting graph, the percolation properties of the graph and the graph distance between remote pairs of vertices. The model interpolates between long-range percolation and inhomogeneous random graphs, and is shown to inherit the interesting features of both these model classes.

I will describe a model for inhomogeneous long-range percolation on Z^d with potential applications in network modeling. Each vertex is independently assigned a non-negative random weight and the probability that there is an edge between two given vertices is then determined by a certain function of their weights and of the distance between them. The results concern the degree distribution in the resulting graph, the percolation properties of the graph and the graph distance between remote pairs of vertices. The model interpolates between long-range percolation and inhomogeneous random graphs, and is shown to inherit the interesting features of both these model classes.

**12/5, Andras Balint: The critical value function in the divide and colour model**

Abstract:

The divide and colour model is a simple and natural stochastic model for dependent colourings of the vertex set of an infinite graph. This model has two parameters: an edge-parameter p, which determines how strongly the states of different vertices depend on each other, and a colouring parameter r, which is the probability of colouring a given vertex red. For each value of p, there exists a critical colouring value R such that there is almost surely no infinite red cluster for all r infinite red cluster exists with positive probability for all r>R. In this talk, I will discuss some new results, obtained jointly with Vincent Beffara and Vincent Tassion, concerning different properties, such as (non-)continuity and (non-)monotonicity, of the critical colouring value as a function of the edge-parameter, as well as both deterministic and probabilistic bounds on the critical colouring value.

The divide and colour model is a simple and natural stochastic model for dependent colourings of the vertex set of an infinite graph. This model has two parameters: an edge-parameter p, which determines how strongly the states of different vertices depend on each other, and a colouring parameter r, which is the probability of colouring a given vertex red. For each value of p, there exists a critical colouring value R such that there is almost surely no infinite red cluster for all r infinite red cluster exists with positive probability for all r>R. In this talk, I will discuss some new results, obtained jointly with Vincent Beffara and Vincent Tassion, concerning different properties, such as (non-)continuity and (non-)monotonicity, of the critical colouring value as a function of the edge-parameter, as well as both deterministic and probabilistic bounds on the critical colouring value.

**26/5, Vitali Wachtel, Mathematical Institute, LMU, München: Random walks in Weyl chambers**

Abstract:

We construct $k$-dimensional random walks conditioned to stay in a Weyl chamber at all times. The chief difficulty is to find a harmonic function for a random walk. It turns out that one needs different approaches under different moment assumptions on unconditioned random walks. We prove also limit theorems for random walks confined to a Weyl chamber.

We construct $k$-dimensional random walks conditioned to stay in a Weyl chamber at all times. The chief difficulty is to find a harmonic function for a random walk. It turns out that one needs different approaches under different moment assumptions on unconditioned random walks. We prove also limit theorems for random walks confined to a Weyl chamber.

**31/5, Jenny Jonasson: Discussion seminar - Can we use extreme value theory to analyse data from naturalistic driving studies**

Abstract:

The idea behind naturalistic driving studies is that ordinary people drives cars that are equipped with a number of measuring devices such as cameras both on the road and on the driver, radars, accelerometers, etc. The main question concerns accident prevention. Although the amount of data is enormous there are still not many accidents in the data sets and therefore near-accidents are also extracted from the data. Our task is to decide if accidents and near-accidents are similar in some sense. Near-accidents and accidents can be thought of as extreme events and hence we use extreme value theory.

The idea behind naturalistic driving studies is that ordinary people drives cars that are equipped with a number of measuring devices such as cameras both on the road and on the driver, radars, accelerometers, etc. The main question concerns accident prevention. Although the amount of data is enormous there are still not many accidents in the data sets and therefore near-accidents are also extracted from the data. Our task is to decide if accidents and near-accidents are similar in some sense. Near-accidents and accidents can be thought of as extreme events and hence we use extreme value theory.

**7/6, Chris Glasbey, Biomathematics & Statistics Scotland: Dynamic programming versus graph cut algorithms for fitting non-parametric models to image data**

Abstract:

Image restoration, segmentation and template matching are generic problems in image processing that can often be formulated as non-parametric model fitting: maximising a penalised likelihood or Bayesian posterior probability for an I-dimensional array of B-dimensional vectors. The global optimum can be found by dynamic programming provided I=1, with no restrictions on B, whereas graph cut algorithms require B=1 and a convex smoothness penalty, but place no restrictions on I. I compare conditions and results for the two algorithms, using restoration of a synthetic aperture radar (SAR) image for illustration.

Image restoration, segmentation and template matching are generic problems in image processing that can often be formulated as non-parametric model fitting: maximising a penalised likelihood or Bayesian posterior probability for an I-dimensional array of B-dimensional vectors. The global optimum can be found by dynamic programming provided I=1, with no restrictions on B, whereas graph cut algorithms require B=1 and a convex smoothness penalty, but place no restrictions on I. I compare conditions and results for the two algorithms, using restoration of a synthetic aperture radar (SAR) image for illustration.

**16/6, Stefan Hoberg and Malin Persson: Optimal design for pharmacokinetic trials**(Master thesis presentation)

Abstract:

When performing a pharmacokinetic study one measures the concentration of the drug several times. When, and how many times to do this, is not always easy to determine. Using optimal design theory, this thesis will show a method to find an optimal number of measurements and also the times to conduct them. The robustness of this design will be investigated by shifting the design points to determine if that will have a big effect on the estimations of the parameter values. For the model used in this thesis a design with three different design points was the optimal one. The second and third time points proved to be unaffected by most shifts on the times. If the first design point was moved close to or past the time when the concentration is at its maximum, problems appeared. This resulted in difficulties obtaining estimates for the parameters, and the ones acquired proved to be unreliable.

When performing a pharmacokinetic study one measures the concentration of the drug several times. When, and how many times to do this, is not always easy to determine. Using optimal design theory, this thesis will show a method to find an optimal number of measurements and also the times to conduct them. The robustness of this design will be investigated by shifting the design points to determine if that will have a big effect on the estimations of the parameter values. For the model used in this thesis a design with three different design points was the optimal one. The second and third time points proved to be unaffected by most shifts on the times. If the first design point was moved close to or past the time when the concentration is at its maximum, problems appeared. This resulted in difficulties obtaining estimates for the parameters, and the ones acquired proved to be unreliable.

**1/9, Ilya Molchanov, University of Bern, Switzerland: Partially identified models and random sets**

Abstract:

A statistical model is partially identified if it does not make possible to come up with a unique estimate of the unknown parameter, even if the sample size grows to infinity. The talk presents several examples of such models related to interval regression, statistical analysis of games and treatment response and explains how tools from the theory of random sets can be used to provide a unified solution to all these problems.

A statistical model is partially identified if it does not make possible to come up with a unique estimate of the unknown parameter, even if the sample size grows to infinity. The talk presents several examples of such models related to interval regression, statistical analysis of games and treatment response and explains how tools from the theory of random sets can be used to provide a unified solution to all these problems.

**4/10, Mari Myllymäki, Aalto University, Finland: Testing of mark independence for marked point patterns**

Abstract:

The talk discusses the testing of independence of marks for marked point patterns. Many researchers use for this purpose the popular envelope test. However, this may lead to unreasonably high type I error probabilities, because in this test spatial correlations are inspected for a range of distances simultaneously. Alternatively, the deviation test can be used, but it says only little about the reason of rejection of the null hypothesis. In this talk, it is demonstrated how the envelope test can be refined so that it becomes both a valuable tool for statistical inference and for understanding the reasons of possible rejections of the independence hypothesis. This is joint work with Pavel Grabarnik and Dietrich Stoyan.

The talk discusses the testing of independence of marks for marked point patterns. Many researchers use for this purpose the popular envelope test. However, this may lead to unreasonably high type I error probabilities, because in this test spatial correlations are inspected for a range of distances simultaneously. Alternatively, the deviation test can be used, but it says only little about the reason of rejection of the null hypothesis. In this talk, it is demonstrated how the envelope test can be refined so that it becomes both a valuable tool for statistical inference and for understanding the reasons of possible rejections of the independence hypothesis. This is joint work with Pavel Grabarnik and Dietrich Stoyan.

**6/10, Maria Deijfen, Stockholm University: Stable bigamy on the line**

Abstract:

Consider a vertex set that consists of the points of a Poisson process on R^d. How should one go about to obtain a translation invariant random graph with a prescribed degree distribution on this vertex set? When does the resulting graph percolate? One natural way of constructing the graph is based on the Gale-Shapley stable marriage, and the question of percolation has then turned out to be surprisingly difficult to answer. I will describe some existing results and a number of open problems, with focus on the case d=1 and constant degree 2. (Joint work with Olle Häggström, Alexander Holroyd and Yuval Peres.)

Consider a vertex set that consists of the points of a Poisson process on R^d. How should one go about to obtain a translation invariant random graph with a prescribed degree distribution on this vertex set? When does the resulting graph percolate? One natural way of constructing the graph is based on the Gale-Shapley stable marriage, and the question of percolation has then turned out to be surprisingly difficult to answer. I will describe some existing results and a number of open problems, with focus on the case d=1 and constant degree 2. (Joint work with Olle Häggström, Alexander Holroyd and Yuval Peres.)

**20/10, Martin S Ridout, University of Kent, UK: Numerical Laplace transform inversion for statisticians**

Abstract:

We review some methods of inverting Laplace transforms numerically, focusing on methods that can be implemented effectively in statistical packages such as R. We argue that these algorithms are sufficiently fast and reliable to be used within iterative statistical inference procedures. Illustrative examples cover calculation of tail probabilities, random number generation and non-Gaussian AR(1) models.

We review some methods of inverting Laplace transforms numerically, focusing on methods that can be implemented effectively in statistical packages such as R. We argue that these algorithms are sufficiently fast and reliable to be used within iterative statistical inference procedures. Illustrative examples cover calculation of tail probabilities, random number generation and non-Gaussian AR(1) models.

**27/10, Jorge Mateu, Department of Mathematics, University Jaume I, Castellon, Spain: Functional spatial statistics with a focus on geostatistics and point processes**

Abstract:

Observing complete functions as a result of random experiments is nowadays possible by the development of real-time measurement instruments and data storage resources. Functional data analysis deals with the statistical description and modeling of samples of random functions. Functional versions for a wide range of statistical tools have been recently developed. Here we are interested in the case of functional data presenting spatial dependence, and the problem is handled from the geostatistical and point process contexts. Functional kriging prediction and clustering are developed. Additionally, we propose functional global and local marked second-order characteristics.

Observing complete functions as a result of random experiments is nowadays possible by the development of real-time measurement instruments and data storage resources. Functional data analysis deals with the statistical description and modeling of samples of random functions. Functional versions for a wide range of statistical tools have been recently developed. Here we are interested in the case of functional data presenting spatial dependence, and the problem is handled from the geostatistical and point process contexts. Functional kriging prediction and clustering are developed. Additionally, we propose functional global and local marked second-order characteristics.

**26/10, Erik Mellegård: Obtaining Origin/Destination-matrices from cellular network data**

Abstract:

"Mobile devices in America are generating something like 600 billion geo-spatially tagged transactions per day" says Jeff Jonas, chief scientist at IBM. A lot of this data are passing through the mobile operators systems and are collected for billing and networking purposes. This data could be used to obtain valuable information about people's movements, something that is not being done today. The main reason for this is that the operators are afraid of what would happen if someone would mistreat this data and used if to track people. This thesis presents a method for ﬁnding Origin/ Destination-matrices from the mobile network data in a way that keeps the individuals' privacy. Since the operators are reluctant to let us used any real data, the method has been applied to synthetic data and some call data records. The results of this thesis shows that it is feasible to obtain Origin/Destination-matrices from mobile network data.

"Mobile devices in America are generating something like 600 billion geo-spatially tagged transactions per day" says Jeff Jonas, chief scientist at IBM. A lot of this data are passing through the mobile operators systems and are collected for billing and networking purposes. This data could be used to obtain valuable information about people's movements, something that is not being done today. The main reason for this is that the operators are afraid of what would happen if someone would mistreat this data and used if to track people. This thesis presents a method for ﬁnding Origin/ Destination-matrices from the mobile network data in a way that keeps the individuals' privacy. Since the operators are reluctant to let us used any real data, the method has been applied to synthetic data and some call data records. The results of this thesis shows that it is feasible to obtain Origin/Destination-matrices from mobile network data.

**10/11, Adam Andersson, Malliavin's differential calculus for random variables**

Abstract:

I will present a simplified version of what is called Malliavin calculus. In probability theory, random variables are commonly defined on an abstract probability space, with minimal assumptions on the space. Here we choose the topology of the probability space to be the n-dimensional Euclidean space equipped with its Borel sigma-field and a Gaussian measure. Defining a smooth class of random variables, that are differentiable in the underlying chance parameter of the probability space, we develop a differential calculus. With some effort, this is extended to somehow less smooth random variables. As an application I will discuss the existence of densities for random vectors, by looking att properties of the so called Malliavin matrix. The nice thing with this simplified setting is that it makes the differential calculus very clear. Moreover the proofs of some key results are identical to those in the case of an abstract probability space. While all the material is basic and known, the presentation of the subject in this simple form, is hardly found in the literature. The talk is a polished copy of the PhD seminar I gave in the spring.

I will present a simplified version of what is called Malliavin calculus. In probability theory, random variables are commonly defined on an abstract probability space, with minimal assumptions on the space. Here we choose the topology of the probability space to be the n-dimensional Euclidean space equipped with its Borel sigma-field and a Gaussian measure. Defining a smooth class of random variables, that are differentiable in the underlying chance parameter of the probability space, we develop a differential calculus. With some effort, this is extended to somehow less smooth random variables. As an application I will discuss the existence of densities for random vectors, by looking att properties of the so called Malliavin matrix. The nice thing with this simplified setting is that it makes the differential calculus very clear. Moreover the proofs of some key results are identical to those in the case of an abstract probability space. While all the material is basic and known, the presentation of the subject in this simple form, is hardly found in the literature. The talk is a polished copy of the PhD seminar I gave in the spring.

**17/11, Jeffrey Steif, The behaviour of the lower tail of the distribution of a supercritical branching process at a fixed large time**

Abstract:

We discuss the above and in addition how a supercritical branching process behaves when it survives to a large fixed time but has much smaller size than expected. This is certainly all well known (by some) but there is a nice picture. I wanted to understand this myself since it serves as a 'toy model' for how the spectrum for critical percolation behaves; however, I won't discuss this latter thing.

We discuss the above and in addition how a supercritical branching process behaves when it survives to a large fixed time but has much smaller size than expected. This is certainly all well known (by some) but there is a nice picture. I wanted to understand this myself since it serves as a 'toy model' for how the spectrum for critical percolation behaves; however, I won't discuss this latter thing.

**1/12, David Belius, ETH, Zürich, Switzerland: Fluctuations of certain cover times**

Abstract:

It is expected that the fluctuations of the cover times of several families of graphs converge to the Gumbel extreme value distribution. However this has been proven in only a few cases and remains open for e.g. the discrete torus in dimensions three and higher. In my talk I will present a recent result that proves Gumbel fluctuations in a different but closely related setting (namely the discrete cylinder), using the theory of random interlacements as a tool.

It is expected that the fluctuations of the cover times of several families of graphs converge to the Gumbel extreme value distribution. However this has been proven in only a few cases and remains open for e.g. the discrete torus in dimensions three and higher. In my talk I will present a recent result that proves Gumbel fluctuations in a different but closely related setting (namely the discrete cylinder), using the theory of random interlacements as a tool.