language: en

Adaptive Markov Chain Monte Carlo through Regeneration

Walter R. Gilks
Medical Research Council Biostatistics Unit
Cambridge, CB2 2SR, UK.
Gareth O. Roberts
Statistical Laboratory University of Cambridge
Cambridge, CB2 1SB, UK.
Sujit K. Sahu
School of Mathematics University of Wales, Cardiff
Cardiff, CF2 4YH, UK.
January 26, 1998

Summary Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution . This is done by calculating averages over the sample path of a Markov chain having as its stationary distribution. For computational efficiency, the Markov chain should be rapidly mixing. This can sometimes be achieved only by careful design of the transition kernel of the chain, on the basis of a detailed preliminary exploratory analysis of . An alternative approach might be to allow the transition kernel to adapt whenever new features of are encountered during the MCMC run. However, if such adaptation occurs infinitely often, the stationary distribution of the chain may be disturbed. We describe a framework, based on the concept of Markov chain regeneration, which allows adaptation to occur infinitely often, but which does not disturb the stationary distribution of the chain or the consistency of sample-path averages.

Key Words: Adaptive method; Bayesian inference; Gibbs sampling; Markov chain Monte Carlo;