Abstract. 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.

The problem of detection and identification of an unobservable change in the distribution of a random sequence is studied via a hidden Markov model (HMM) approach. The formulation is Bayesian, on-line, discrete-time, allowing both single-and multiple-disorder cases, dealing with both independent and identically distributed (i.i.d.) and dependent observations scenarios, allowing for statistical dependencies between the change-time and change-type in both the observation sequence and the risk structure, and allowing for general discrete-time disorder distributions. Several of these factors provide useful new generalizations of the sequential analysis theory for change detection and/or hypothesis testing, taken individually. In this paper, a unifying framework is provided that handles each of these considerations not only individually, but also concurrently. Optimality results and optimal decision characterizations are given as well as detailed examples that illustrate the myriad of sequential change detection and identification problems that fall within this new framework. Disciplines Finance | Finance and Financial ManagementThis journal article is available at ScholarlyCommons: http://repository.upenn.edu/fnce_papers/347 DETECTION AND IDENTIFICATION OF AN UNOBSERVABLE CHANGE IN THE DISTRIBUTION OF A MARKOV-MODULATED RANDOM SEQUENCE SAVAS DAYANIK AND CHRISTIAN GOULDINGAbstract. The problem of detection and diagnosis of an unobservable change in the distribution of a random sequence is studied via a hidden Markov model approach. The formulation is Bayesian, on-line, discrete-time, allowing both single-and multiple-disorder cases, dealing with both i.i.d. and dependent observations scenarios, allowing for statistical dependencies between the change-time and change-type in both the observation sequence and the risk structure, and allowing for general discrete-time disorder distributions. Several of these factors provide useful new generalizations of the sequential analysis theory for change detection and/or hypothesis testing, taken individually. In this paper, a unifying framework is provided that handles each of these considerations not only individually, but also concurrently. Optimality results and optimal decision characterizations are given as well as detailed examples that illustrate the myriad of sequential change detection and diagnosis problems that fall within this new framework.

This paper examines the joint problem of detection and identification of a sudden and unobservable change in the probability distribution function (pdf) of a sequence of independent and identically distributed (i.i.d.) random variables to one of finitely many alternative pdf's. The objective is quick detection of the change and accurate inference of the ensuing pdf. Following a Bayesian approach, a new sequential decision strategy for this problem is revealed and is proven optimal. Geometrical properties of this strategy are demonstrated via numerical examples.