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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.
Original language | English |
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Pages (from-to) | 494-529 |
Number of pages | 36 |
Journal | Bernoulli |
Volume | 22 |
Issue number | 1 |
Early online date | 30 Sept 2015 |
DOIs | |
Publication status | Published - 1 Feb 2016 |
Keywords
- convergence
- hidden Markov mode
- particle filters
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Dive into the research topics of 'On the role of interaction in sequential Monte Carlo algorithms'. Together they form a unique fingerprint.Projects
- 1 Finished
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Sequential Monte Carlo in Random Environments
Whiteley, N. (Principal Investigator)
5/08/13 → 5/02/15
Project: Research
Profiles
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Professor Nick Whiteley
- School of Mathematics - Heilbronn Chair in Data Science
- Statistical Science
Person: Member, Academic , Member