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Limit theorems for sequential MCMC methods
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Finke, Axel, Doucet, Arnaud and Johansen, Adam M. (2020) Limit theorems for sequential MCMC methods. Advances in Applied Probability, 52 (2). pp. 377-403. doi:10.1017/apr.2020.9 ISSN 0001-8678.
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WRAP-Limit-theorems-sequential-MCMC-Johansen-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1144Kb) | Preview |
Official URL: https://doi.org/10.1017/apr.2020.9
Abstract
Both sequential Monte Carlo (SMC) methods (a.k.a. ‘particle filters’) and sequential Markov chain Monte Carlo (sequential MCMC) methods constitute classes of algorithms which can be used to approximate expectations with respect to (a sequence of) probability distributions and their normalising constants. While SMC methods sample particles conditionally independently at each time step, sequential MCMC methods sample particles according to a Markov chain Monte Carlo (MCMC) kernel. Introduced over twenty years ago in [6], sequential MCMC methods have attracted renewed interest recently as they empirically outperform SMC methods in some applications. We establish an -inequality (which implies a strong law of large numbers) and a central limit theorem for sequential MCMC methods and provide conditions under which errors can be controlled uniformly in time. In the context of state-space models, we also provide conditions under which sequential MCMC methods can indeed outperform standard SMC methods in terms of asymptotic variance of the corresponding Monte Carlo estimators.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Mathematical statistics, Monte Carlo method, Stochastic processes -- Mathematical models, Time-series analysis, Limit theorems (Probability theory) | |||||||||
Journal or Publication Title: | Advances in Applied Probability | |||||||||
Publisher: | Applied Probability Trust | |||||||||
ISSN: | 0001-8678 | |||||||||
Official Date: | June 2020 | |||||||||
Dates: |
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Volume: | 52 | |||||||||
Number: | 2 | |||||||||
Page Range: | pp. 377-403 | |||||||||
DOI: | 10.1017/apr.2020.9 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Advances in Applied Probability [http://doi.org/10.1017/apr.2020.9 This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder. | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 15 January 2020 | |||||||||
Date of first compliant Open Access: | 15 January 2021 | |||||||||
RIOXX Funder/Project Grant: |
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