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The iterated auxiliary particle filter
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Guarniero, Pieralberto, Johansen, Adam M. and Lee, Anthony (2017) The iterated auxiliary particle filter. Journal of the American Statistical Association, 112 (520). pp. 1636-1647. doi:10.1080/01621459.2016.1222291 ISSN 0162-1459.
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Official URL: http://dx.doi.org/10.1080/01621459.2016.1222291
Abstract
We present an offline, iterated particle filter to facilitate statistical inference in general state space hidden Markov models. Given a model and a sequence of observations, the associated marginal likelihood L is central to likelihood-based inference for unknown statistical parameters. We define a class of “twisted” models: each member is specified by a sequence of positive functions ψ and has an associated ψ-auxiliary particle filter that provides unbiased estimates of L. We identify a sequence ψ∗ that is optimal in the sense that the ψ∗-auxiliary particle filter’s estimate of L has zero variance. In practical applications, ψ∗ is unknown so the ψ∗ -auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate ψ∗ , and demonstrate empirically that the resulting iterated auxiliary particle filter significantly outperforms the bootstrap particle filter in challenging settings. Applications include parameter estimation using a particle Markov chain Monte Carlo algorithm
| Item Type: | Journal Article | ||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||
| Library of Congress Subject Headings (LCSH): | Markov processes, Monte Carlo method | ||||||||||
| Journal or Publication Title: | Journal of the American Statistical Association | ||||||||||
| Publisher: | American Statistical Association | ||||||||||
| ISSN: | 0162-1459 | ||||||||||
| Official Date: | 18 July 2017 | ||||||||||
| Dates: |
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| Volume: | 112 | ||||||||||
| Number: | 520 | ||||||||||
| Page Range: | pp. 1636-1647 | ||||||||||
| DOI: | 10.1080/01621459.2016.1222291 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||
| Date of first compliant deposit: | 3 August 2016 | ||||||||||
| Date of first compliant Open Access: | 26 August 2017 | ||||||||||
| Adapted As: |
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