Adaptive Gibbs samplers and related MCMC methods

TL;DR

This paper investigates adaptive Gibbs samplers that modify their parameters during execution, highlighting potential convergence issues and providing conditions under which convergence can be guaranteed.

Contribution

It introduces adaptive Gibbs and Metropolis-within-Gibbs algorithms, analyzes their convergence properties, and offers conditions for ensuring their reliability.

Findings

Adaptive Gibbs samplers can fail to converge without proper safeguards.

Certain conditions guarantee convergence of adaptive Gibbs methods.

The paper provides examples and theoretical results on adaptive MCMC algorithms.

Abstract

We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run by learning as they go in an attempt to optimize the algorithm. We present a cautionary example of how even a simple-seeming adaptive Gibbs sampler may fail to converge. We then present various positive results guaranteeing convergence of adaptive Gibbs samplers under certain conditions.