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Asymptotically optimal Bayesian sequential change detection and identification rules

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  • Savas Dayanik
  • Warren Powell
  • Kazutoshi Yamazaki

Abstract

We study the joint problem of sequential change detection and multiple hypothesis testing. Suppose that the common distribution of a sequence of i.i.d. random variables changes suddenly at some unobservable time to one of finitely many distinct alternatives, and one needs to both detect and identify the change at the earliest possible time. We propose computationally efficient sequential decision rules that are asymptotically either Bayes-optimal or optimal in a Bayesian fixed-error-probability formulation, as the unit detection delay cost or the misdiagnosis and false alarm probabilities go to zero, respectively. Numerical examples are provided to verify the asymptotic optimality and the speed of convergence. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:p:337-370:10.1007/s10479-012-1121-6
    DOI: 10.1007/s10479-012-1121-6
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    References listed on IDEAS

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    1. Apostolos N. Burnetas & Michael N. Katehakis, 1997. "Optimal Adaptive Policies for Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 222-255, February.
    2. Savas Dayanik & Christian Goulding & H. Vincent Poor, 2008. "Bayesian Sequential Change Diagnosis," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 475-496, May.
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    Cited by:

    1. Pergamenchtchikov, Serguei M. & Tartakovsky, Alexander G. & Spivak, Valentin S., 2022. "Minimax and pointwise sequential changepoint detection and identification for general stochastic models," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. 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.

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