Detection and identification of changes of hidden Markov chains: Asymptotic theory

Date
2021-10-06
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Source Title
Statistical Inference for Stochastic Processes
Print ISSN
1387-0874
Electronic ISSN
1572-9311
Publisher
Springer Science and Business Media B.V.
Volume
25
Issue
2
Pages
261 - 301
Language
English
Type
Article
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Abstract

This paper revisits a unified framework of sequential change-point detection and hypothesis testing modeled using hidden Markov chains and develops its asymptotic theory. Given a sequence of observations whose distributions are dependent on a hidden Markov chain, the objective is to quickly detect critical events, modeled by the first time the Markov chain leaves a specific set of states, and to accurately identify the class of states that the Markov chain enters. We propose computationally tractable sequential detection and identification strategies and obtain sufficient conditions for the asymptotic optimality in two Bayesian formulations. Numerical examples are provided to confirm the asymptotic optimality. © 2021, The Author(s).

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Keywords
Asymptotic optimality, Change point detection, Hidden Markov models, Hypothesis testing, Optimal stopping
Citation
Published Version (Please cite this version)