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

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  • Savas Dayanik

    (Bilkent University)

  • Kazutoshi Yamazaki

    (Kansai University)

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.

Suggested Citation

  • Savas Dayanik & Kazutoshi Yamazaki, 2022. "Detection and identification of changes of hidden Markov chains: asymptotic theory," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 261-301, July.
    • Handle: RePEc:spr:sistpr:v:25:y:2022:i:2:d:10.1007_s11203-021-09253-5
    DOI: 10.1007/s11203-021-09253-5
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    References listed on IDEAS

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    1. Pergamenchtchikov, Serguei & Tartakovsky, Alexander G., 2019. "Asymptotically optimal pointwise and minimax change-point detection for general stochastic models with a composite post-change hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    2. Serguei Pergamenchtchikov & Alexander G. Tartakovsky, 2018. "Asymptotically optimal pointwise and minimax quickest change-point detection for dependent data," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 217-259, April.
    3. Savas Dayanik & Christian Goulding & H. Vincent Poor, 2008. "Bayesian Sequential Change Diagnosis," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 475-496, May.
    4. Savas Dayanik & Warren B. Powell & Kazutoshi Yamazaki, 2013. "Asymptotically optimal Bayesian sequential change detection and identification rules," Annals of Operations Research, Springer, vol. 208(1), pages 337-370, September.
    5. Alexander Tartakovsky, 1998. "Asymptotic Optimality of Certain Multihypothesis Sequential Tests: Non‐i.i.d. Case," Statistical Inference for Stochastic Processes, Springer, vol. 1(3), pages 265-295, October.
    6. Savas Dayanik & Warren Powell & Kazutoshi Yamazaki, 2013. "Asymptotically optimal Bayesian sequential change detection and identification rules," Annals of Operations Research, Springer, vol. 208(1), pages 337-370, September.
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    Cited by:

    1. Linda Boudjemila & Alexander Bobyl & Vadim Davydov & Vladislav Malyshkin, 2022. "On a Moving Average with Internal Degrees of Freedom," Papers 2211.14075, arXiv.org.

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