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On the role of interaction in sequential Monte Carlo algorithms
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Whiteley, Nick, Lee, Anthony and Heine, Kari (2015) On the role of interaction in sequential Monte Carlo algorithms. Bernoulli, 22 (1). pp. 494-529. doi:10.3150/14-BEJ666 ISSN 1350-7265.
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Official URL: http://doi.org/10.3150/14-BEJ666
Abstract
We introduce a general form of sequential Monte Carlo algorithm defined in terms of a parameterized resampling mechanism. We find that a suitably generalized notion of the Effective Sample Size (ESS), widely used to monitor algorithm degeneracy, appears naturally in a study of its convergence properties. We are then able to phrase sufficient conditions for time-uniform convergence in terms of algorithmic control of the ESS, in turn achievable by adaptively modulating the interaction between particles. This leads us to suggest novel algorithms which are, in senses to be made precise, provably stable and yet designed to avoid the degree of interaction which hinders parallelization of standard algorithms. As a byproduct we prove time-uniform convergence of the popular adaptive resampling particle filter.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Bernoulli | ||||
Publisher: | Int Statistical Institute | ||||
ISSN: | 1350-7265 | ||||
Official Date: | 30 September 2015 | ||||
Dates: |
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Volume: | 22 | ||||
Number: | 1 | ||||
Page Range: | pp. 494-529 | ||||
DOI: | 10.3150/14-BEJ666 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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