Stability of sequential Monte Carlo samplers via the Foster–Lyapunov condition

Sequential Monte Carlo (SMC) samplers [Del Moral, P., Doucet, A., Jasra, A., 2006. Sequential Monte Carlo samplers. J. Roy. Statist. Soc. B 68, 411–436] are designed to simulate from a sequence of probability measures on a common measurable space ( E , E ) . One way to measure the accuracy of the re...

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Bibliographic Details
Published inStatistics & probability letters Vol. 78; no. 17; pp. 3062 - 3069
Main Authors Jasra, Ajay, Doucet, Arnaud
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.12.2008
Elsevier
SeriesStatistics & Probability Letters
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Summary:Sequential Monte Carlo (SMC) samplers [Del Moral, P., Doucet, A., Jasra, A., 2006. Sequential Monte Carlo samplers. J. Roy. Statist. Soc. B 68, 411–436] are designed to simulate from a sequence of probability measures on a common measurable space ( E , E ) . One way to measure the accuracy of the resulting Monte Carlo estimates is the asymptotic variance in the central limit theorem (CLT). We investigate the conditions, for algorithms used in practice, which are sufficient to ensure that the resulting expression is upper bounded, of which, the typical conditions (e.g. [Chopin, N., 2004. Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist. 32, 2385–2411]) are quite restrictive. We use the Foster–Lyapunov condition and contractions in the f -norm of the Markov kernels [Douc, R., Moulines, E., Rosenthal, J.S., 2004. Quantitative bounds on convergence of time-inhomogeneous Markov chains. Ann. Appl. Probab. 14, 1643–1665] to establish quantitative bounds on the asymptotic variance.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2008.05.023