Multihypothesis sequential probability ratio tests. II. Accurate asymptotic expansions for the expected sample size

Dragalin, Vladimir; Tartakovsky, Alexander G.; Veeravalli, Venugopal V.

doi:10.1109/18.850677

Cited by 94 publications

(73 citation statements)

References 26 publications

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“…Foundational studies include the non-Bayesian (minimax) formulation proposed by Lorden [21] and the Bayesian formulation proposed by Shiryayev [27] for sequential change detection and the papers of Wald and Wolfowitz [28] and Arrow, Blackwell, and Girshick [1] on sequential hypothesis testing. We refer the reader to Basseville and Nikiforov [3], Dragalin, Tartakovsky, and Veeravalli [10,11], and Lai [17,19] and the references therein for detailed background on these topics, recent developments, and discussion of applications. Despite the progress that has been made in these areas, the literature offers few non-asymptotic optimality results and provides for the most part very limited models of the general problem, and hence many important considerations have remained open.…”

Section: Introduction Contributions and Related Workmentioning

confidence: 99%

Sequential Detection and Identification of a Change in the Distribution of a Markov-Modulated Random Sequence

Dayanık

Goulding

2009

IEEE Trans. Inform. Theory

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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.

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Section: Introduction Contributions and Related Workmentioning

confidence: 99%

Sequential Detection and Identification of a Change in the Distribution of a Markov-Modulated Random Sequence

Dayanık

Goulding

2009

IEEE Trans. Inform. Theory

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“…Both change detection and sequential multi-hypothesis testing have been studied extensively. For recent reviews of these areas, we refer the reader to Basseville and Nikiforov [3], Dragalin, Tartakovsky and Veeravalli [8,9], and Lai [14], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Sequential Change Diagnosis

2008

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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.

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“…In neuro-science and psychology, humans [4] and animals [14] are often modeled as maximizing the long-run average reward rate, or the ratio of accuracy to expected temporal delay. In computer science and engineering modeling, the speed-accuracy trade-off is typically formalized in terms of Bayes-risk minimization, which minimizes a linear combination of expected temporal delay and response errors [18,16,10,11,15,9,8,12]. The advantage of the risk minimization formulation is that the linear speed-accuracy trade-off makes it amenable to a substantial body of tools for solving or characterizing the optimal solution, including Wald's sequential statistical decision formulation [17] and Bellman's dynamic programming principle [1].…”

Section: Introductionmentioning

confidence: 99%

Reward-Rate Maximization in Sequential Identification under a Stochastic Deadline

Dayanık¹,

Yu²

2013

SIAM J. Control Optim.

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Abstract. Any intelligent system performing evidence-based decision making under time pressure must negotiate a speed-accuracy trade-off. In computer science and engineering, this is typically modeled as minimizing a Bayes-risk functional that is a linear combination of expected decision delay and expected terminal decision loss. In neuroscience and psychology, however, it is often modeled as maximizing the long-term reward rate, or the ratio of expected terminal reward and expected decision delay. The two approaches have opposing advantages and disadvantages. While Bayes-risk minimization can be solved with powerful dynamic programming techniques unlike reward-rate maximization, it also requires the explicit specification of the relative costs of decision delay and error, which is obviated by reward-rate maximization. Here, we demonstrate that, for a large class of sequential multihypothesis identification problems under a stochastic deadline, the reward-rate maximization is equivalent to a special case of Bayes-risk minimization, in which the optimal policy that attains the minimal risk when the unit sampling cost is exactly the maximal reward rate is also the policy that attains maximal reward rate. We show that the maximum reward rate is the unique unit sampling cost for which the expected total observation cost and expected terminal reward break even under every Bayes-risk optimal decision rule. This interplay between reward-rate maximization and Bayesrisk minimization formulations allows us to show that maximum reward rate is always attained. We can compute the policy that maximizes reward rate by solving an inverse Bayes-risk minimization problem, whereby we know the Bayes risk of the optimal policy and need to find the associated unit sampling cost parameter. Leveraging this equivalence, we derive an iterative dynamic programming procedure for solving the reward-rate maximization problem exponentially fast, thus incorporating the advantages of both the reward-rate maximization and Bayes-risk minimization formulations. As an illustration, we will apply the procedure to a two-hypothesis identification example.

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Multihypothesis sequential probability ratio tests. II. Accurate asymptotic expansions for the expected sample size

Cited by 94 publications

References 26 publications

Sequential Detection and Identification of a Change in the Distribution of a Markov-Modulated Random Sequence

Sequential Detection and Identification of a Change in the Distribution of a Markov-Modulated Random Sequence

Bayesian Sequential Change Diagnosis

Reward-Rate Maximization in Sequential Identification under a Stochastic Deadline

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