Multi-Chart Detection Procedure for Bayesian Quickest Change-Point Detection with Unknown Post-Change Parameters

In this paper, the problem of quickly detecting an abrupt change on a stochastic process under Bayesian framework is considered. Different from the classic Bayesian quickest change-point detection problem, this paper considers the case where there is uncertainty about the post-change distribution. Specifically, the observer only knows that the post-change distribution belongs to a parametric distribution family but he does not know the true value of the post-change parameter. In this scenario, we propose two multi-chart detection procedures, termed as M-SR procedure and modified M-SR procedure respectively, and show that these two procedures are asymptotically optimal when the postchange parameter belongs to a finite set and are asymptotically ǫ−optimal when the post-change parameter belongs to a compact set with finite measure. Both algorithms can be calculated efficiently as their detection statistics can be updated recursively. We then extend the study to consider the multisource monitoring problem with unknown post-change parameters. When those monitored sources are mutually independent, we propose a window-based modified M-SR detection procedure and show that the proposed detection method is first-order asymptotically optimal when post-change parameters belong to finite sets. We show that both computation and space complexities of the proposed algorithm increase only linearly with respect to the number of sources. The work of J. Geng is supported by the National Natural Science Foundation of China under grant 61601144 and by the Fundamental Research Funds for the Central Universities under grant AUGA5710013915. The work of E. Bayraktar is supported in part by the NSF under grant number DMS-1613170 and in part by the Susan M. Smith Professorship. The work of L. Lai is supported by the National Science Foundation under grants CNS-1660128 and ECCS-1711468. This paper was presented in part at IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Shanghai, China, Mar. 2016 [1]. J. Geng is with the School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin, 150001, China (Email: [email protected]). E. Bayraktar is with the Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA (Email:[email protected]). L. Lai is with the Department of Electrical and Computer Engineering, University of California, Davis, CA, 95616, USA (Email: [email protected]). August 24, 2017 DRAFT