Central limit theorem for sequential Monte Carlo methods and its application to bayesian inference

• 成果类型: Article
• 署名作者: Chopin, N
• 署名单位: University of Bristol
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000698
• 发表日期: 2004
• 页码: 2385-2411
• 关键词: particle filter; approximation; STABILITY

摘要

The term sequential Monte Carlo methods or, equivalently, particle filters, refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (pi(t)). We establish in this paper a central limit theorem for the Monte Carlo estimates produced by these computational methods. This result holds under minimal assumptions on the distributions pi(t), and applies in a general framework which encompasses most of the sequential Monte Carlo methods that have been considered in the literature, including the resample-move algorithm of Gilks and Berzuini [J. R. Stat. Soc. Ser B Stat. Methodol. 63 (2001) 127-146] and the residual resampling scheme. The corresponding asymptotic variances provide a convenient measurement of the precision of a given particle filter. We study, in particular, in some typical examples of Bayesian applications, whether and at which rate these asymptotic variances diverge in time, in order to assess the long term reliability of the considered algorithm.