• Bernoulli
  • Volume 18, Number 1 (2012), 252-278.

On adaptive resampling strategies for sequential Monte Carlo methods

Pierre Del Moral, Arnaud Doucet, and Ajay Jasra

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Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the convergence analysis of a class of SMC methods where the times at which resampling occurs are computed online 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. By combining semigroup techniques with an original coupling argument, we obtain functional central limit theorems and uniform exponential concentration estimates for these algorithms.

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Bernoulli, Volume 18, Number 1 (2012), 252-278.

First available in Project Euclid: 20 January 2012

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random resampling sequential Monte Carlo methods


Del Moral, Pierre; Doucet, Arnaud; Jasra, Ajay. On adaptive resampling strategies for sequential Monte Carlo methods. Bernoulli 18 (2012), no. 1, 252--278. doi:10.3150/10-BEJ335.

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  • [1] Cappé, O., Moulines, E. and Rydén, T. (2005). Inference in Hidden Markov Models. New York: Springer.
  • [2] Cornebise, J. (2009). Adaptive sequential Monte Carlo methods. Ph.D. thesis, Dept. Applied Mathematics, Univ. Paris 6.
  • [3] Cornebise, J., Moulines, É. and Olsson, J. (2008). Adaptive methods for sequential importance sampling with application to state space models. Stat. Comput. 18 461–480.
  • [4] Del Moral, P. (2004). Feynman–Kac Formulae: Genealogical and Interacting Particle Systems with Applications. New York: Springer.
  • [5] Del Moral, P. and Miclo, L. (2000). Branching and interacting particle systems approximations of Feynman–Kac formulae with applications to non-linear filtering. In Séminaire de Probabilités XXXIV. Lecture Notes in Math. 1729 1–145. Berlin: Springer.
  • [6] Douc, R. and Moulines, E. (2008). Limit theorems for weighted samples with applications to sequential Monte Carlo methods. Ann. Statist. 36 2344–2376.
  • [7] Doucet, A., de Freitas, N. and Gordon, N. (2001). Sequential Monte Carlo Methods in Practice. New York: Springer.
  • [8] Liu, J.S. (2001). Monte Carlo Strategies in Scientific Computing. New York: Springer.
  • [9] Liu, J.S. and Chen, R. (1995). Blind deconvolution via sequential imputation. J. Amer. Statist. Assoc. 90 567–576.