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Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo
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Koskela, Jere, Spanò, Dario and Jenkins, Paul (2018) Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo. Statistics and Computing, 28 (1). pp. 131-144. doi:10.1007/s11222-017-9722-1 ISSN 0960-3174.
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Official URL: http://dx.doi.org/10.1007/s11222-017-9722-1
Abstract
We present a sequential Monte Carlo algorithm for Markov chain trajectories with proposals constructed in reverse time, which is advantageous when paths are conditioned to end in a rare set. The reverse time proposal distribution is constructed by approximating the ratio of Green's functions in Nagasawa's formula. Conditioning arguments can be used to interpret these ratios as low-dimensional conditional sampling distributions of some coordinates of the process given the others. Hence the difficulty in designing SMC proposals in high dimension is greatly reduced. We illustrate our method on estimating an overflow probability in a queueing model, the probability that a diffusion follows a narrowing corridor, and the initial location of an infection in an epidemic model on a network.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
| Library of Congress Subject Headings (LCSH): | Time reversal, Monte Carlo method, Markov processes, Algorithms | |||||||||
| Journal or Publication Title: | Statistics and Computing | |||||||||
| Publisher: | Springer | |||||||||
| ISSN: | 0960-3174 | |||||||||
| Official Date: | January 2018 | |||||||||
| Dates: |
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| Volume: | 28 | |||||||||
| Number: | 1 | |||||||||
| Page Range: | pp. 131-144 | |||||||||
| DOI: | 10.1007/s11222-017-9722-1 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 9 January 2017 | |||||||||
| Date of first compliant Open Access: | 24 January 2018 | |||||||||
| RIOXX Funder/Project Grant: |
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