The Annals of Applied Probability

Perfect sampling for nonhomogeneous Markov chains and hidden Markov models

Nick Whiteley and Anthony Lee

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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.

Article information

Source
Ann. Appl. Probab. Volume 26, Number 5 (2016), 3044-3077.

Dates
Received: October 2014
Revised: December 2015
First available in Project Euclid: 19 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1476884311

Digital Object Identifier
doi:10.1214/15-AAP1169

Mathematical Reviews number (MathSciNet)
MR3563201

Zentralblatt MATH identifier
1353.60067

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

Keywords
Coupling conditional ergodicity nonhomogeneous Markov chains perfect simulation

Citation

Whiteley, Nick; Lee, Anthony. Perfect sampling for nonhomogeneous Markov chains and hidden Markov models. Ann. Appl. Probab. 26 (2016), no. 5, 3044--3077. doi:10.1214/15-AAP1169. https://projecteuclid.org/euclid.aoap/1476884311


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