The Annals of Statistics
- Ann. Statist.
- Volume 32, Number 6 (2004), 2385-2411.
Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference
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 (πt). 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 πt, 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.
Ann. Statist., Volume 32, Number 6 (2004), 2385-2411.
First available in Project Euclid: 7 February 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 65C05: Monte Carlo methods 62F15: Bayesian inference 60F05: Central limit and other weak theorems
Secondary: 82C80: Numerical methods (Monte Carlo, series resummation, etc.) 62L10: Sequential analysis
Chopin, Nicolas. Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist. 32 (2004), no. 6, 2385--2411. doi:10.1214/009053604000000698. https://projecteuclid.org/euclid.aos/1107794873