On the Ergodicity Properties of some Adaptive MCMC Algorithms

C Andrieu, E Moulines

Research output: Contribution to journalArticle (Academic Journal)

140 Citations (Scopus)

Abstract

In this paper we study the ergodicity properties of some adaptive Monte Carlo Markov chain algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a so-called adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit theorem. We prove that the conditions required are satisfied for the Independent Metropolis-Hastings algorithm and the Random Walk Metropolis algorithm with symmetric increments. Finally we propose an application of these results to the case where the proposal distribution of the Metropolis-Hastings update is a mixture of distributions from a curved exponential family.
Original languageEnglish
Pages (from-to)1462 - 1505
Number of pages44
JournalAnnals of Applied Probability
Volume16 (3)
DOIs
Publication statusPublished - Aug 2006

Bibliographical note

Publisher: Institute of Mathematical Statistics

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