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Twisted particle filters
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Whiteley, Nick and Lee, Anthony (2014) Twisted particle filters. The Annals of Statistics, Volume 42 (Number 1). pp. 115-141. doi:10.1214/13-AOS1167 ISSN 0090-5364.
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Official URL: http://dx.doi.org/10.1214/13-AOS1167
Abstract
We investigate sampling laws for particle algorithms and the influence
of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. Among a broad class of candidates we characterize the essentially unique family of particle system transition kernels which is optimal with respect to an asymptotic-in-time variance growth rate criterion. The sampling structure of the algorithm defined by these optimal transitions turns out to be only subtly different from standard algorithms and yet the fluctuation properties of the estimates it provides can be dramatically different. The structure of the optimal transition suggests a new class of algorithms, which we term “twisted” particle filters and which we validate with asymptotic analysis of a more traditional nature, in the regime where the number of particles tends to infinity.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
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Journal or Publication Title: | The Annals of Statistics | ||||||||
Publisher: | Institute of Mathematical Statistics | ||||||||
ISSN: | 0090-5364 | ||||||||
Official Date: | February 2014 | ||||||||
Dates: |
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Volume: | Volume 42 | ||||||||
Number: | Number 1 | ||||||||
Page Range: | pp. 115-141 | ||||||||
DOI: | 10.1214/13-AOS1167 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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