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Bayesian Sequential Change Diagnosis

Department of Operations Research and Financial Engineering and the Bendheim Center for Finance, Princeton University, Princeton, New Jersey 08544
Department of Operations Research and Financial Engineering, Princeton, New Jersey 08544
School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08544
sdayanik{at}princeton.edu, http://www.princeton.edu/sdayanik
cgouldin{at}princeton.edu
poor{at}princeton.edu, http://www.ee.princeton.edu/bios/poorbio.html

Sequential change diagnosis is the joint problem of detection and identification of a sudden and unobservable change in the distribution of a random sequence. In this problem, the common probability law of a sequence of i.i.d. random variables suddenly changes at some disorder time to one of finitely many alternatives. This disorder time marks the start of a new regime, whose fingerprint is the new law of observations. Both the disorder time and the identity of the new regime are unknown and unobservable. The objective is to detect the regime-change as soon as possible, and, at the same time, to determine its identity as accurately as possible. Prompt and correct diagnosis is crucial for quick execution of the most appropriate measures in response to the new regime, as in fault detection and isolation in industrial processes, and target detection and identification in national defense. The problem is formulated in a Bayesian framework. An optimal sequential decision strategy is found, and an accurate numerical scheme is described for its implementation. Geometrical properties of the optimal strategy are illustrated via numerical examples. The traditional problems of Bayesian change-detection and Bayesian sequential multi-hypothesis testing are solved as special cases. In addition, a solution is obtained for the problem of detection and identification of component failure(s) in a system with suspended animation.

Key Words: Bayesian sequential change detection and identification; optimal stopping; Markov chains
History: Received: November 21, 2006; revision received: October 25, 2007;