2014

Abstracts, see below.

30/1, Andrea Ghiglietti, Milan University, A two-colour Randomly Reinforced Urn design targeting fixed allocations
6/2, David Bolin, Chalmers, Multivariate latent Gaussian random field mixture models
13/2, Ege Rubak, Aalborg University, Denmark, Determinantal point processes - statistical modeling and inference
20/2, ​Anthony Metcalfe, KTH, Universality classes of lozenge tilings of a polyhedron
27/2, Sergei Zuyev, Chalmers, Discussion seminar: Probing harmony with algebra (or attractiveness with statistics)
6/3, Tuomas Rajala, Chalmers, ​Denoising polar ice data using point pattern statistics
13/3, Pierre Nyqvist, KTH, Importance sampling through a min-max representation for viscosity solutions to Hamilton-Jacobi equations
20/3, Arvind Singh, Orsay, Localization of a vertex-reinforced random walk on Z
27/3, Terence P. Speed, Walter and Eliza Hall Institute of Medical Research, Melbourne, and University of California, Berkeley, Normalizing omic data
8/4, Aernout van Enter, Groningen, The Netherlands, Bootstrap percolation, the role  of anisotropy:  Questions, some answers and applications
10/4, Rasmus Waagepetersen, Aalborg university, Denmark, ​Quasi-likelihood for spatial point processes
24/4, Oleg Seleznjev, Umeå University, Linear approximation of random processes with variable smoothness
8/5, ​Ted Cox, Syracuse University, ​Convergence of finite voter model densities
15/5, Marie-Colette van Lieshaut, CWI, The Netherlands, ​A Spectral Mean for Point Sampled Closed Curves
20/5, ​Simo Särkkä, Aalto University, Finland, Theory and Practice of Particle Filtering for State Space Models
27/5, Nanny Wermuth, Johannes Gutenberg University Mainz, Traceable regressions: general properties and some special cases
5/6, Alexey Lindo, Non-parametric inference for infinitely divisible distributions and Levy processes
12/6, F. C. Klebaner, Monas University, Melbourne, ​When is a Stochastic Exponential of a Martingale a true Martingale?
2/9, Pavel Grabarnik, Laboratory of Ecosystems Modeling, the Russian Academy of Sciences, Spatial complexity of ecosystems: testing models for spatial point patterns
18/9, Jean-François Coeurjolly, LJK, Grenoble, Stein's estimation of the intensity of a stationary spatial Poisson point
25/9, ​Natalya Smorodina, St. Petersburg State University, Limit theorems for symmetric random walks and probabilistic approximation of the Cauchy problem solution for Schrödinger type  evolution equations
30/9, Holger Drees, Hamburg University, Improved Estimation of the Distribution of a Tail Chain
30/9, Anja Janssen, Hamburg University, Asymptotic Independence of Stochastic Volatility Models
2/10, ​Vadim Shcherbakov, Royal Holloway, University of London, Long term behaviour of locally interacting birth-and-death processes
16/10, ​Peter Guttorp, University of Washington, USA, Comparing regional climate models to weather data
23/10, Tomasz Kozubowski, University of Nevada, USA, Certain bivariate distributions and random processes connected with maxima and minima
6/11, ​Torgny Lindvall, Chalmers, On coupling of certain Markov Processes
13/11, Giacomo Zanella, University of Warwick, UK, Bayesian complementary clustering, MCMC and Anglo-Saxon placenames
20/11, Mikhail Lifshits, St. Petersburg State University, Least energy functions and pursuits accompanying Wiener process
27/11, Jennifer Wadsworth, University of Cambridge, Likelihood-based inference for max-stable processes: some recent developments
2/12, ​David Perrett, Perception Lab, St Andrews University, UK, Statistical analysis of visual cues underlying facial attractiveness
4/12, Anna Kiriliouk, Université Catholique de Louvain, An M-estimator of spatial tail dependence
11/12, Nibia Aires, Astellas Pharma, Leiden, Statistics in drug development, what happens after submission?
16/12, Sören Christensen, Kiel, Representation Results for Excessive Functions and Application to Stochastic Control Problems
18/12, Professor Mark van de Wiel, Vrije Universiteit Amsterdam, How to learn from a lot: Empirical Bayes in Genomics
18/12, Lars Rönnegård, Dalarna University, Hierarchical generalized linear models – a Lego approach to mixed models

 

 
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.
 
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).
 
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.
 
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].
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.
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.
 
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.
 
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.
 
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.
 
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.
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.

Published: Mon 25 Feb 2019.