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Teoriya Veroyatnostei i ee Primeneniya, 2004, Volume 49, Issue 3, Pages 538–582
DOI: https://doi.org/10.4213/tvp207
(Mi tvp207)
 

This article is cited in 181 scientific papers (total in 181 papers)

General asymptotic Bayesian theory of quickest change detection

A. G. Tartakovskiia, V. Veeravallib

a University of Southern California
b University of Illinois at Urbana-Champaign
References:
Abstract: The optimal detection procedure for detecting changes in independent and identically distributed (i.i.d.) sequences in a Bayesian setting was derived by Shiryaev in the 1960s sixties. However, the analysis of the performance of this procedure in terms of the average detection delay and false alarm probability has been an open problem. In this paper, we develop a general asymptotic change-point detection theory that is not limited to a restrictive i.i.d. assumption. In particular, we investigate the performance of the Shiryaev procedure for general discrete-time stochastic models in the asymptotic setting, where the false alarm probability approaches zero. We show that the Shiryaev procedure is asymptotically optimal in the general non-i.i.d. case under mild conditions. We also show that the two popular non-Bayesian detection procedures, namely the Page and the Shiryaev–Roberts–Pollak procedures, are generally not optimal (even asymptotically) under the Bayesian criterion. The results of this study are shown to be especially important in studying the asymptotics of decentralized change detection procedures.
Keywords: change-point detection, sequential detection, asymptotic optimality, nonlinear renewal theory.
Received: 07.11.2003
English version:
Theory of Probability and its Applications, 2005, Volume 49, Issue 3, Pages 458–497
DOI: https://doi.org/10.1137/S0040585X97981202
Bibliographic databases:
Language: English
Citation: A. G. Tartakovskii, V. Veeravalli, “General asymptotic Bayesian theory of quickest change detection”, Teor. Veroyatnost. i Primenen., 49:3 (2004), 538–582; Theory Probab. Appl., 49:3 (2005), 458–497
Citation in format AMSBIB
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\paper General asymptotic Bayesian theory of
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\transl
\jour Theory Probab. Appl.
\yr 2005
\vol 49
\issue 3
\pages 458--497
\crossref{https://doi.org/10.1137/S0040585X97981202}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000232261200006}
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  • https://www.mathnet.ru/eng/tvp207
  • https://doi.org/10.4213/tvp207
  • https://www.mathnet.ru/eng/tvp/v49/i3/p538
  • This publication is cited in the following 181 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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