Analysis of Convergence Rates of Some Gibbs Samplers on Continuous State Spaces

TL;DR

This paper analyzes the convergence rates of certain Gibbs samplers on continuous state spaces using coupling techniques and modifications of finite Markov chain methods.

Contribution

It introduces a novel approach to analyze convergence of Gibbs samplers on continuous spaces, extending finite Markov chain techniques.

Findings

Derived convergence rate bounds for Gibbs samplers on continuous spaces

Applied coupling methods to non-Markovian chains

Extended analysis to generalized Gibbs sampling algorithms

Abstract

We use a non-Markovian coupling and small modifications of techniques from the theory of finite Markov chains to analyze some Markov chains on continuous state spaces. The first is a Gibbs sampler on narrow contingency tables, the second a gen- eralization of a sampler introduced by Randall and Winkler.