On the ergodicity properties of some adaptive MCMC algorithms

• 成果类型: Article
• 署名作者: Andrieu, Christophe; Moulines, Eric
• 署名单位: University of Bristol; IMT - Institut Mines-Telecom; IMT Atlantique
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000286
• 发表日期: 2006
• 页码: 1462-1505
• 关键词: metropolis algorithms; em algorithm; stochastic-approximation; Poisson equation; CONVERGENCE; hastings; rates

摘要

In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo 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.