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Sequential Quasi Monte Carlo

Gerber, Mathieu, Chopin, Nicolas·2015·Journal of the Royal Statistical Society Series B: Statistical Methodology
DOI 10.1111/rssb.12104
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Abstract

Summary: We derive and study sequential quasi Monte Carlo (SQMC), a class of algorithms obtained by introducing QMC point sets in particle filtering. SQMC is related to, and may be seen as an extension of, the array-RQMC algorithm of L'Ecuyer and his colleagues. The complexity of SQMC is O{Nlog(N)}, where N is the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo rate OP(N−1/2). The only requirement to implement SQMC algorithms is the ability to write the simulation of particle xtn given xt−1n as a deterministic function of xt−1n and a fixed number of uniform variates. We show that SQMC is amenable to the same extensions as standard SMC, such as forward smoothing, backward smoothing and unbiased likelihood evaluation. In particular, SQMC may replace SMC within a particle Markov chain Monte Carlo algorithm. We establish several convergence results. We provide numerical evidence that SQMC may significantly outperform SMC in practical scenarios.

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Metadata

Authors
Gerber, M., & Chopin, N.
Affiliations
  • Université de Lausanne, Switzerland, and Centre de Recherche en Economie et Statistique , Paris , France
  • Centre de Recherche en Economie et Statistique and Ecole Nationale de la Statistique et de l’Administration Economique , Paris , France
Venue
Journal of the Royal Statistical Society Series B: Statistical Methodology
Publisher
Oxford University Press (OUP)
Published
2015-05-12
Volume
77
Issue
3
Pages
509-579
ISSN
  • 1369-7412
  • 1467-9868
DOI
10.1111/rssb.12104
Cited by
93
References
1
Language
en
Licence
academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
Funders
Agence Nationale de la Recherche (ANR-11-LABEX-0047)

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