A generalized change detection problem

Nikiforov, Igor

doi:10.1109/18.370109

Cited by 138 publications

(81 citation statements)

References 15 publications

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“…Perhaps the closest sequential decision problem our model relates to is a generalization of the change-point problem, often called the 'detection and isolation problem,' introduced by Nikiforov in 1995 (see [11], [10] and [2] for a survey). A process Y 1 , Y 2 , .…”

Section: Problem Formulation and Backgroundmentioning

confidence: 99%

Communication Under Strong Asynchronism

Tchamkerten

Chandar

Wornell

2009

IEEE Trans. Inform. Theory

108

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We consider asynchronous communication over point-to-point discrete memoryless channels without feedback. The transmitter starts sending one block codeword at an instant that is uniformly distributed within a certain time period, which represents the level of asynchronism. The receiver, by means of a sequential decoder, must isolate the message without knowing when the codeword transmission starts but being cognizant of the asynchronism level. We are interested in how quickly can the receiver isolate the sent message, particularly in the regime where the asynchronism level is exponentially larger than the codeword length, which we refer to as 'strong asynchronism. ' This model of sparse communication might represent the situation of a sensor that remains idle most of the time and, only occasionally, transmits information to a remote base station which needs to quickly take action. Because of the limited amount of energy the sensor possesses, assuming the same cost per transmitted symbol, it is of interest to consider minimum size codewords given the asynchronism level.The first result is an asymptotic characterization of the largest asynchronism level, in terms of the codeword length, for which reliable communication can be achieved: vanishing error probability can be guaranteed as the codeword length N tends to infinity while the asynchronism level grows as e N α if and only if α does not exceed the synchronization threshold, a constant that admits a simple closed form expression, and is at least as large as the capacity of the synchronized channel.The second result is the characterization of a set of achievable strictly positive rates in the regime where the asynchronism level is exponential in the codeword length, and where the rate is defined with respect to the expected (random) delay between the time information starts being emitted until the time the receiver makes a decision. Interestingly, this achievability result is obtained by a coding strategy whose decoder not only operates in an asynchronously, but has an almost universal decision rule, in the sense that it is almost independent of the channel statistics.As an application of the first result we consider antipodal signaling over a Gaussian additive channel and derive a simple necessary condition between blocklength, asynchronism level, and SNR for achieving reliable communication.

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Section: Problem Formulation and Backgroundmentioning

confidence: 99%

Communication Under Strong Asynchronism

Tchamkerten

Chandar

Wornell

2009

IEEE Trans. Inform. Theory

108

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“…Yet, the literature has been sparse along this direction. The first results regarding the extension of the sequential change detection problem to include the diagnosis task are given by Nikiforov [25] and Lai [18] in a non-Bayesian framework. Dayanik, Goulding, and Poor [9] study the extension in a Bayesian framework, albeit under the assumption of statistical independence between the disorder and its cause.…”

Section: 2mentioning

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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“…Nikiforov [16] provides the first results for this problem, showing asymptotic optimality for a certain non-Bayesian approach, and Lai [13] generalizes these results through the development of information-theoretic bounds and the application of likelihood methods. In this paper, we follow a Bayesian approach to reveal a new sequential decision strategy for this problem, which incorporates a priori knowledge regarding the distributions of the change time θ and of the change index µ.…”

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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A generalized change detection problem

Cited by 138 publications

References 15 publications

Communication Under Strong Asynchronism

Communication Under Strong Asynchronism

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

Bayesian Sequential Change Diagnosis

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