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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

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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:
DateEvent
October 2016Published
29 December 2015Available
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
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