Adaptive Gibbs samplers

TL;DR

This paper explores adaptive Gibbs samplers that modify their parameters during execution to optimize performance, highlighting both potential pitfalls and conditions for guaranteed convergence.

Contribution

It introduces adaptive Gibbs sampling methods that learn and adjust during runtime, providing convergence guarantees under specific conditions.

Findings

Adaptive Gibbs samplers can fail to converge without proper safeguards.

Certain conditions ensure convergence of adaptive Gibbs algorithms.

The paper offers both cautionary examples and positive convergence results.

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 optimise 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.