Asymptotically optimal Bayesian sequential change detection and identification rules |
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Authors: | Savas Dayanik Warren B Powell Kazutoshi Yamazaki |
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Institution: | 1. Departments of Industrial Engineering and Mathematics, Bilkent University, Bilkent, 06800, Ankara, Turkey 2. Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ, 08544, USA 3. Center for the Study of Finance and Insurance, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka, 560-8531, Japan
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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. |
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