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Perfect sampling for nonhomogeneous Markov chains and hidden Markov models
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Whiteley, Nick and Lee, Anthony (2016) Perfect sampling for nonhomogeneous Markov chains and hidden Markov models. Annals of Applied Probability, 26 (5). pp. 3044-3077. 1476884311. doi:10.1214/15-AAP1169
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Official URL: http://dx.doi.org/10.1214/15-AAP1169
Abstract
We obtain a perfect sampling characterization of weak ergodicity
for backward products of finite stochastic matrices, and equivalently,
simultaneous tail triviality of the corresponding nonhomogeneous
Markov chains. Applying these ideas to hidden Markov models, we
show how to sample exactly from the finite-dimensional conditional
distributions of the signal process given infinitely many observations,
using an algorithm which requires only an almost surely finite number
of observations to actually be accessed. A notion of “successful”
coupling is introduced and its occurrence is characterized in terms
of conditional ergodicity properties of the hidden Markov model and
related to the stability of nonlinear filters.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Statistics | ||||||
| Library of Congress Subject Headings (LCSH): | Markov processes, Stochastic matrices, Perfect simulation (Statistics) | ||||||
| Journal or Publication Title: | Annals of Applied Probability | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 1050-5164 | ||||||
| Official Date: | October 2016 | ||||||
| Dates: |
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| Volume: | 26 | ||||||
| Number: | 5 | ||||||
| Page Range: | pp. 3044-3077 | ||||||
| Article Number: | 1476884311 | ||||||
| DOI: | 10.1214/15-AAP1169 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access | ||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||
| Grant number: | EP/K023330/1 | ||||||
| Related URLs: | |||||||
| Open Access Version: |
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