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Minimax and pointwise sequential changepoint detection and identification for general stochastic models

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  • Pergamenchtchikov, Serguei M.
  • Tartakovsky, Alexander G.
  • Spivak, Valentin S.

Abstract

This paper considers the problem of joint change detection and identification assuming multiple composite post-change hypotheses. We propose a multihypothesis changepoint detection-identification procedure that controls the probabilities of false alarm and wrong identification. We show that the proposed procedure is asymptotically minimax and pointwise optimal, minimizing moments of the detection delay as probabilities of false alarm and wrong identification approach zero. The asymptotic optimality properties hold for general stochastic models with dependent and nonidentically distributed observations. We illustrate general results for detection-identification of changes in multistream Markov ergodic processes. We consider several examples, including an application to rapid detection-identification of COVID-19 in Italy. Our proposed sequential algorithm allows much faster detection of COVID-19 than standard methods.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000203
    DOI: 10.1016/j.jmva.2022.104977
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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 & 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.
    4. 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.
    5. Galtchouk, L. & Pergamenshchikov, S., 2013. "Uniform concentration inequality for ergodic diffusion processes observed at discrete times," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 91-109.
    Full references (including those not matched with items on IDEAS)

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