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 Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 3, Pages 472–499 (Mi tvp2443)

Asymptotic Optimality in Bayesian Changepoint Detection Problems under Global False Alarm Probability Constraint

A. G. Tartakovskii

University of Southern California

Abstract: In the 1960s Shiryaev developed the Bayesian theory of changepoint detection in independent and identically distributed (i.i.d.) sequences. In Shiryaev's classical setting the goal is to minimize an average delay to detection under the constraint imposed on the average probability of false alarm. Recently, Tartakovsky and Veeravalli [Theory Probab. Appl., 49 (2005), pp. 458–497] developed a general Bayesian asymptotic changepoint detection theory (in the classical setting) that is not limited to a restrictive i.i.d. assumption. It was proved that Shiryaev's detection procedure is asymptotically optimal under traditional average false alarm probability constraint, assuming that this probability is small. In the present paper, we consider a less conventional approach where the constraint is imposed on the global, supremum false alarm probability. An asymptotically optimal Bayesian change detection procedure is proposed and thoroughly evaluated for both i.i.d. and non-i.i.d. models when the global false alarm probability approaches zero.

Keywords: asymptotic optimality, changepoint detection, cumulative sum procedure, global false alarm probability, nonlinear renewal theory, Shiryaev's rule, sequential detection.

DOI: https://doi.org/10.4213/tvp2443

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English version:
Theory of Probability and its Applications, 2009, 53:3, 443–466

Bibliographic databases:

Citation: A. G. Tartakovskii, “Asymptotic Optimality in Bayesian Changepoint Detection Problems under Global False Alarm Probability Constraint”, Teor. Veroyatnost. i Primenen., 53:3 (2008), 472–499; Theory Probab. Appl., 53:3 (2009), 443–466

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tvp2443
• https://doi.org/10.4213/tvp2443
• http://mi.mathnet.ru/eng/tvp/v53/i3/p472

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Verdier G., Hilgert N., Vila J.-P., “Optimality of CUSUM rule approximations in change-point detection problems: application to nonlinear state-space systems”, IEEE Trans. Inform. Theory, 54:11 (2008), 5102–5112
2. Polunchenko A.S. Tartakovsky A.G., “State-of-the-art in sequential change-point detection”, Methodol. Comput. Appl. Probab., 14:3 (2012), 649–684
3. Chen J., Zhang W., Poor H.V., “On Parallel Sequential Change Detection Controlling False Discovery Rate”, 2016 50Th Asilomar Conference on Signals, Systems and Computers, Conference Record of the Asilomar Conference on Signals Systems and Computers, ed. Matthews M., IEEE Computer Soc, 2016, 107–111
4. Chronopoulou A., Nagi R., “Online Community Detection For Fused Social Network Graphs”, 2016 19Th International Conference on Information Fusion (Fusion), IEEE, 2016, 1682–1686
5. Han D. Tsung F. Xian J., “On the Optimality of Bayesian Change-Point Detection”, Ann. Stat., 45:4 (2017), 1375–1402
6. Nitzan E. Halme T. Koivunen V., “Bayesian Methods For Multiple Change-Point Detection With Reduced Communication”, IEEE Trans. Signal Process., 68 (2020), 4871–4886
7. Ford J.J. James J. Molloy T.L., “On the Informativeness of Measurements in Shiryaev'S Bayesian Quickest Change Detection”, Automatica, 111 (2020), 108645
8. Halme T., Nitzan E., Poor H.V., Koivunen V., “Bayesian Multiple Change-Point Detection With Limited Communication”, 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, International Conference on Acoustics Speech and Signal Processing Icassp, IEEE, 2020, 5490–5494
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