Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference
Nicolas Chopin
Source: Ann. Statist. Volume 32, Number 6
(2004), 2385-2411.
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 (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.
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Keywords: Markov chain Monte Carlo; particle filter; recursive Monte Carlo filter; resample-move algorithms; residual resampling; state-space model
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1107794873
Digital Object Identifier: doi:10.1214/009053604000000698
Mathematical Reviews number (MathSciNet): MR2153989
Zentralblatt MATH identifier: 1079.65006
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