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News

PhD Student: The Institute for Mathematical Stochastics (Prof. Dr. Anja Sturm) seeks qualified applicants for the position of a PhD student starting on or after February 01, 2018 for the duration of three years (more information is available here).


Student assistant: The Institute for Mathematical Stochastics (Prof. Dr. Axel Munk) seeks a student assistant for the Research Training Group 2088 in the project A1 “Wasserstein Metrics in Statistics: Inference”, starting on or after January 1, 2018 (for more details see here).


Next talk in the Stochastics Colloquium:
25.10.2017, 11:15, Dr. Vlada Limic (Université de Strasbourg)

"What is a uniform distribution?" (Abstract).
Statistics Meets Friends: The workshop "Statistics Meets Friends - from biophysics to inverse problems and back -" takes place in Göttingen from November 29th to December 1st, 2017.
Schuhmacher

Spatial Stochastics

Members of the research group

Prof. Dr. Dominic Schuhmacher (publications)
Henning Höllwarth, Dipl.-Math. (publications)
Fabian Kück, M.Sc.

(Publikationen)

Jörn Schrieber, M.Sc.

(Publikationen)


PhD Students

• Henning Höllwarth, Dipl.-Math., topic: Statistical inference in point process models

(Publikationen)

• Jörn Schrieber, M.Sc., topic: Optimal transport in probability and statistics,
joint supervision with Prof. Dr. Anita Schöbel

(Publikationen)

Former PhD Students

• Dr. Fabian Kück, Convergence Rates in Dynamic Network Models (2017)

(Publikationen)

• Dr. Kaspar Stucki, Invariance properties and approximation results for point processes (2013),
joint supervision with Prof. Ilya Molchanov

(Publikationen)

M.Sc. Students

• Yi Zhao, M.Sc. student, topic: A probabilistic look at mutual information with application to point process

(Publikationen)

Former M.Sc. and B.Sc. Students

• Xueqiu Feng, M.Sc., Selective Importance Sampling for Computing the Maximum Likelihood Estimator in Point Process Models (2017)

(Publikationen)

• Janne Breiding, B.Sc., Comparison of logistic regression and maximum pseudolikelihood for spatial point processes (2017)

(Publikationen)

• Oskar Hallmann, M.Sc., Convergence Rates for Point Processes Thinned by Logit-Gaussian Random Fields (2016)

(Publikationen)

• Florian Heinemann, B.Sc., Metropolis-Hastings algorithms for spatial point processes (2016)

(Publikationen)

• Valentin Hartmann, B.Sc., A Geometry-Based Approach for Solving the Transportation Problem with Euclidean Cost (2016)

(Publikationen)

• Stephan Meyer, M.Sc., Maximum likelihood estimation of exponential families of stochastic processes (2016)

(Publikationen)

• Philipp Möller, M.Sc., Maximum Likelihood Estimation for Spatial Point Processes using Monte Carlo Methods (2016)

(Publikationen)

• Burcu Coskun, M.Sc., Statistical Inference of Linear Birth-And-Death Processes (2015)

(Publikationen)

• Saskia Schwedes, M.Sc., Konvergenzgeschwindigkeit für Markov-Chain Monte Carlo (2015)

(Publikationen)

• Xueqiu Feng, B.Sc., A comprehensive overview of linear birth-and-death processes with an outlook to the non-linear case (2015)

(Publikationen)

• Clemens Steinhaus, B.Sc., Limit Behaviour of Discrete Models in Financial Mathematics (2015)

(Publikationen)

• Anna Klünker, M.Sc., Tests auf Unabhängigkeit zwischen Punkten und Marken (2015)

(Publikationen)

• Alexander Moehrs, B.Sc., Gaußsche Zufallsfelder: Differenzierbarkeit von Pfaden (2015)

(Publikationen)

• Philipp Möller, B.Sc., Shuffling measures and the total variation distance to a perfectly randomized deck of cards (2014)

(Publikationen)

• Maria Heuer, M.Sc., Thinning of point processes by [0,1]-transformed Gaussian random fields (2014)

(Publikationen)

• Björn Bähre, B.Sc., Numerical computation of L2-Wasserstein distance between images (2014)

(Publikationen)

• Nicolas Lenz, B.Sc., Universität Bern, Additivity and Ortho-Additivity in Gaussian Random Fields (2013), joint supervision with Dr. David Ginsbourger

(Publikationen)

• Jan Schwiderowski, B.Sc., Erwartete Treffzeiten in Markovketten und deren Anwendung auf Glücksspiele mit Sicherungsoption (2013)

(Publikationen)


Research topics

Optimal transport in probability and statistics

How different are two spatial structures? This may be answered very generally in terms of the minimum "cost" incurred when transforming one of the objects into the other one. Structures can be anything from images, over point patterns, to geometric bodies. Cost is often specified in terms of (powers of) distances by which (infinitesimal) units of the structure are transported. The picture gives an example of the optimal transportation plan for transforming the underlying grey scale image to a uniform images when using the squared Euclidean distance.



Dynamic random graphs

Dynamic random graphs are a usefull tool to describe complex systems with an underlying network structure which evolves in time. Of particular interest in this area are the asymptotic properties of the dynamic graphs. The spatial structure can be considered to obtain more realistic models for complex systems.

The following images visualize realizations of random graphs in the model by Britton and Lindholm at a fixed time with different distributions for the social indices. Such indices describe the popularity of the nodes (individuals) and are represented by the node sizes.



Continuum percolation for Gibbs point processes

The Boolean model is defined as the union of balls with a fixed radius and center points that form a homogenous Poisson process in R^d (see the picture below). Each connected component is called a cluster. One says that the Boolean model percolates if it contains a cluster with infinite volume (area). It is well known that in dimension larger than or equal to two there exists a critical intensity for the underlying Poisson process below which the Boolean model almost surely does not percolate and above which it almost surely does percolate.

What happens if one replaces the Poisson process with a Gibbs point process? For which models does there exist a similar percolation phase transition, i.e. a critical parameter such that the percolation probability jumps from zero to one?