Central Limit Theorem for sequential Monte Carlo methods and its application to Bayesian inference

NXA Chopin

Research output: Contribution to journalArticle (Academic Journal)peer-review

201 Citations (Scopus)

Abstract

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.
Translated title of the contributionCentral Limit Theorem for sequential Monte Carlo methods and its application to Bayesian inference
Original languageEnglish
Pages (from-to)2385 - 2411
JournalAnnals of Statistics
Volume32 (6)
Publication statusPublished - Dec 2004

Bibliographical note

Publisher: Inst Mathematical Statistics
Other identifier: IDS Number: 901MD

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