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Simple conditions for convergence of sequential Monte Carlo genealogies with applications
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Brown, Suzie, Jenkins, Paul, Johansen, Adam M. and Koskela, Jere (2021) Simple conditions for convergence of sequential Monte Carlo genealogies with applications. Electronic Journal of Probability, 26 . 1. doi:10.1214/20-EJP561 ISSN 1083-6489.
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Official URL: https://doi.org/10.1214/20-EJP561
Abstract
We present simple conditions under which the limiting genealogical process associated with a class of interacting particle systems with non-neutral selection mechanisms, as the number of particles grows, is a time-rescaled Kingman coalescent. Sequential Monte Carlo algorithms are popular methods for approximating integrals in problems such as non-linear filtering and smoothing which employ this type of particle system. Their performance depends strongly on the properties of the induced genealogical process. We verify the conditions of our main result for standard sequential Monte Carlo algorithms with a broad class of low-variance resampling schemes, as well as for conditional sequential Monte Carlo with multinomial resampling.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Statistics |
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Library of Congress Subject Headings (LCSH): | Convergence, Monte Carlo method, Resampling (Statistics) | ||||||||||||
Journal or Publication Title: | Electronic Journal of Probability | ||||||||||||
Publisher: | University of Washington. Dept. of Mathematics | ||||||||||||
ISSN: | 1083-6489 | ||||||||||||
Official Date: | 5 January 2021 | ||||||||||||
Dates: |
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Volume: | 26 | ||||||||||||
Article Number: | 1 | ||||||||||||
DOI: | 10.1214/20-EJP561 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 21 December 2020 | ||||||||||||
Date of first compliant Open Access: | 5 January 2021 | ||||||||||||
RIOXX Funder/Project Grant: |
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