2012


Abstracts
, see below.


19/1, Anna-Kaisa Ylitalo, University of Jyväskylä, Statistical inference for eye movements.
26/1, Chris Jennison, University of Bath, Effective design of Phase II and Phase III trials: an over-arching approach.
2/2, Oleg Rusakov, S:t Petersburg State University, Processes of Poissonian stochastic index and a family of Ornstein-Uhlenbeck type processes.
7/2, Paavo Salminen, Åbo Akademi, Optimal stopping of continuous time Markov processes.
7/2, Juha Alho, University of Eastern Finland, Statistical aspects of mortality modeling.
9/2, Stas Volkov, University of Lund, Forest fires on integers.
16/2, Anton Muratov, Bit Flipping Models.
1/3, Oleg Sysoev, Linköping university, Monotonic regression for large multivariate datasets.
27/3, Tatyana Turova, Lunds University, Bootstrap percolation on some models of random graphs.
17/4, Ronald Meester, Scaling limits in fractal percolation.
19/4, Vladimir Vatutin, Steklov Mathematical Institute, Subcritical branching processes in random environment.
24/4, Krzysztof Bartoszek and Serik Sagitov, Interspecies correlation for randomly evolving traits.
26/4, Elena Dyakonova, Steklov Mathematical Institute, Moscow, Multi-type branching processes in random environment.
3/5, Bruce E. Sagan, Michigan State University, Permutation Patterns and Statistics.
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.
10/5, Reinhard Bürger, Universität Wien, Invasion and sojourn properties of locally beneficial mutations in a two-locus continent-island model of gene flow.
15/5, Mari Myllymäki, Aalto University, Hierarchical modeling of second-order spatial structure of epidermal nerve fiber pattern.
22/5, Amandine Veber, Ecole Polytechnique, Paris (Biomathematics seminar), Evolution in a spatial continuum.
24/5, Amandine Veber, Ecole Polytechnique, Paris, Large-scale behaviour of the spatial Lambda-Fleming-Viot process.
31/5, Mattias Villani, Linköping University, Bayesian Methods for Flexible Modeling of Conditional Distributions.
7/6, Brunella Spinelli and Giacomo Zanella, Chalmers and University of Milan, Stable point processes: statistical inference and generalisations.
4/9, Giacomo Zanella, Warwick University, UK, Branching stable point processes.
6/9, Ilya Molchanov, University of Bern, Switzerland, Invariance properties of random vectors and stochastic processes based on the zonoid concept.
25/9, Prof. Günter Last, Karlsruhe Institute of Technology, Fock space analysis of Poisson functionals - 1 & 2.
27/9, Prof. Günter Last, Karlsruhe Institute of Technology, Fock space analysis of Poisson functionals - 3 & 4.
28/9, Martin Rosvall, Umeå universitet, Mapping change in large networks.
11/10, Nanny Wermuth, Chalmers and International Agency of Research on Cancer, Lyon, France, Traceable regressions applied to the Mannheim study of children at risk.
18/10, Stas Volkov, Lund University, On random geometric subdivisions.
26/10, Malin Östensson, doctoral thesis, Statistical Methods for Genome Wide Association Studies.
1/11, Uwe Rösler, University of Kiel, On Stochastic Fixed Point Equations and the Weighted Branching Process.
8/11, Eugene Mamontov, Chalmers, Non-stationary invariant and dynamic-equilibrium Markov stochastic processes.
13/11, Måns Henningson, Chalmers, Quantum theory and probability.
15/11, Anders Johansson, Gävle, Existence of matchings in random sub-hypergraphs.
22/11, David Bolin, University of Lund, Excursion and contour uncertainty regions for latent Gaussian models.
29/11, Dietrich von Rosen, SLU Uppsala, From univariate linear to multilinear models.
11/12, Jimmy Olsson, Lund University, Metropolising forward particle filtering backward simulation and Rao-Blackwellisation using multiple trajectories.
13/12, Erik Lindström, Lund University, Tuned Iterated Filtering.


 

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.
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.
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
 
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.
 
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.
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.
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
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.
 
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.
 
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.
 
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.
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.
 
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.
 
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)
 
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.
 
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.
 
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.
 
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.
 
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.
 
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.
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.
 
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].
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.
 
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.
 
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.
 
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.
 
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.
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.
 
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).
 
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.
 
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
 
11/12, Jimmy Olsson, Lund University: Metropolising forward particle filtering backward simulation and Rao-Blackwellisation using multiple trajectories
Abstract:
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.

 

Published: Wed 06 Feb 2019.