UBC - University of British Columbia (Vancouver Campus, , 2329 West Mall, Vancouver, BC Canada V6T 1Z4 -
Okanagan Campus, 3333 University Way, Kelowna, BC Canada V1V 1V7 - Canada)
4Statistics - Department of Statistics (DEPARTMENT OF STATISTICS 333-6356 Agricultural Road University of British Columbia Vancouver, BC, V6T 1Z2 Tel: 604 822 0570 Fax: 604 822 6960 - Canada)
UBC - University of British Columbia (Vancouver Campus, , 2329 West Mall, Vancouver, BC Canada V6T 1Z4 -
Okanagan Campus, 3333 University Way, Kelowna, BC Canada V1V 1V7 - Canada)
5Department of Computing [London] (180 Queen's Gate South Kensington Campus Imperial College London London SW7 2AZ - Royaume-Uni)
Abstract : Sequential Monte Carlo (SMC) methods are a general class of techniques to sample approximately from any sequence of probability distributions. These distributions are approximated by a cloud of weighted samples which are propagated over time using a combination of importance sampling and resampling steps. This article is concerned with the convergence analysis of a class of SMC methods where the times at which resampling occurs are computed on-line using criteria such as the effective sample size. This is a popular approach amongst practitioners but there are very few convergence results available for these methods. It is shown here that these SMC algorithms correspond to a particle approximation of a Feynman-Kac flow of measures on adaptive excursion spaces. By combining a non-linear distribution flow analysis to an original coupling technique, we obtain functional central limit theorems and uniform exponential concentration estimates for these algorithms. The original exponential concentration theorems presented in this study significantly improve previous concentration estimates obtained for SMC algorithms.
Type de document :
Article dans une revue
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2012, 18 (1), pp.252-278
https://hal.inria.fr/inria-00332436
Contributeur : Pierre Del Moral
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Soumis le : mercredi 22 octobre 2008 - 18:42:45
Dernière modification le : jeudi 11 janvier 2018 - 06:22:36
Document(s) archivé(s) le : samedi 26 novembre 2016 - 01:57:21
Pierre Del Moral, Arnaud Doucet, Ajay Jasra. On Adaptive Resampling Procedures for Sequential Monte Carlo Methods. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2012, 18 (1), pp.252-278. 〈inria-00332436v4〉
