Geometric convergence of slice sampling

by Viacheslav Natarovskii
Cumulative thesis
Date of Examination:2021-10-14
Date of issue:2021-10-19
Advisor:Prof. Dr. Daniel Jun.-Rudolf
Referee:Prof. Dr. Daniel Jun.-Rudolf
Referee:Prof. Dr. Axel Munk
Persistent Address: http://dx.doi.org/10.53846/goediss-8892

 

 

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Abstract

English

In Bayesian statistics sampling w.r.t. a posterior distribution, which is given through a prior and a likelihood function, is a challenging task. The generation of exact samples is in general quite difficult, since the posterior distribution is often known only up to a normalizing constant. A standard way to approach this problem is a Markov chain Monte Carlo (MCMC) algorithm for approximate sampling w.r.t. the target distribution. In this cumulative dissertation geometric convergence guarantees are given for two different MCMC methods: simple slice sampling and elliptical slice sampling.
Keywords: slice sampling; Markov chain Monte Carlo; elliptical slice sampling; geometric convergence; Wasserstein contraction; spectral gap
 
Statistik