PERFECT SAMPLING FOR NONHOMOGENEOUS MARKOV CHAINS AND HIDDEN MARKOV MODELS

被引：2

作者：

Whiteley, Nick ^{[1
]}

Lee, Anthony ^{[2
]}

机构：

[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

[2] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

来源：

ANNALS OF APPLIED PROBABILITY | 2016年 / 26卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

Coupling; conditional ergodicity; nonhomogeneous Markov chains; perfect simulation; STABILITY;

D O I：

10.1214/15-AAP1169

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：3044 / 3077

页数：34