PERFECT SAMPLING FOR NONHOMOGENEOUS MARKOV CHAINS AND HIDDEN MARKOV MODELS

• 成果类型: Article
• 署名作者: Whiteley, Nick; Lee, Anthony
• 署名单位: University of Bristol; University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1169
• 发表日期: 2016
• 页码: 3044-3077
• 关键词: stability

摘要

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.