Perfect sampling for nonhomogeneous Markov chains and hidden Markov models

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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.
Original languageEnglish
Pages (from-to)3044-3077
Number of pages34
JournalAnnals of Applied Probability
Volume26
Issue number5
DOIs
Publication statusPublished - 19 Oct 2016

Keywords

  • Conditional ergodicity
  • Coupling
  • Nonhomogeneous Markov chains
  • Perfect simulation

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