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

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  • Jasra, Ajay
  • Doucet, Arnaud

Abstract

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 . 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.

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  • Jasra, Ajay & Doucet, Arnaud, 2008. "Stability of sequential Monte Carlo samplers via the Foster-Lyapunov condition," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3062-3069, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:3062-3069
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    References listed on IDEAS

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    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. Nicolas Chopin, 2002. "Central Limit Theorem for Sequential Monte Carlo Methods and its Applications to Bayesian Inference," Working Papers 2002-44, Center for Research in Economics and Statistics.
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    1. Monica Billio & Roberto Casarin, 2010. "Identifying business cycle turning points with sequential Monte Carlo methods: an online and real-time application to the Euro area," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 145-167.

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