TY - JOUR
T1 - Asymptotically optimal Bayesian sequential change detection and identification rules
AU - Dayanik, Savas
AU - Powell, Warren Buckler
AU - Yamazaki, Kazutoshi
N1 - Funding Information:
Acknowledgements The authors thank Alexander Tartakovsky for the illuminating discussions. We also thank an anonymous referee and the editors for the constructive remarks and suggestions which significantly improved our presentation. The research of Savas Dayanik was supported by the TÜB˙TAK Research Grants 109M714 and 110M610. Warren B. Powell was supported in part by the Air Force Office of Scientific Research, contract FA9550-08-1-0195, and the National Science Foundation, contract CMMI-0856153. Kazu-toshi Yamazaki was in part supported by Grant-in-Aid for Young Scientists (B)22710143, the Ministry of Education, Culture, Sports, Science and Technology, and Grant-in-Aid for Scientific Research (B)2271014, Japan Society for the Promotion of Science.
PY - 2013/9
Y1 - 2013/9
N2 - 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.
AB - 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.
KW - Asymptotic optimality
KW - Optimal stopping
KW - Sequential change detection and hypothesis testing
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U2 - 10.1007/s10479-012-1121-6
DO - 10.1007/s10479-012-1121-6
M3 - Article
AN - SCOPUS:84883054457
SN - 0254-5330
VL - 208
SP - 337
EP - 370
JO - Annals of Operations Research
JF - Annals of Operations Research
IS - 1
ER -