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22
GENERAL ASYMPTOTIC BAYESIAN THEORY OF QUICKEST CHANGE DETECTION
, 2004
"... The optimal detection procedure for detecting changes in independent and identically distributed (i.i.d.) sequences in a Bayesian setting was derived by Shiryaev in the nineteen sixties. However, the analysis of the performance of this procedure in terms of the average detection delay and false al ..."
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Cited by 46 (18 self)
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The optimal detection procedure for detecting changes in independent and identically distributed (i.i.d.) sequences in a Bayesian setting was derived by Shiryaev in the nineteen sixties. However, the analysis of the performance of this procedure in terms of the average detection delay and false alarm probability has been an open problem. In this paper, we develop a general asymptotic changepoint detection theory that is not limited to a restrictive i.i.d. assumption. In particular, we investigate the performance of the Shiryaev procedure for general discretetime stochastic models in the asymptotic setting where the false alarm probability approaches zero. We show that the Shiryaev procedure is asymptotically optimal in the general noni.i.d. case under mild conditions. We also show that the two popular nonBayesian detection procedures, namely the Page and the ShiryaevRobertsPollak procedures, are generally not optimal (even asymptotically) under the Bayesian criterion. The results of this study are shown to be especially important in studying the asymptotics of decentralized change detection procedures.
Asymptotic performance of a multichart CUSUM test under false alarm probability constraint
 PROC. 44TH IEEE CONF. ON DECISION AND CONTROL AND THE EUROPEAN CONTROL CONF. (CDCECC’05
, 2005
"... Traditionally the false alarm rate in change point detection problems is measured by the mean time to false detection (or between false alarms). The large values of the mean time to false alarm, however, do not generally guarantee small values of the false alarm probability in a fixed time interval ..."
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Cited by 32 (11 self)
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Traditionally the false alarm rate in change point detection problems is measured by the mean time to false detection (or between false alarms). The large values of the mean time to false alarm, however, do not generally guarantee small values of the false alarm probability in a fixed time interval for any possible location of this interval. In this paper we consider a multichannel (multipopulation) change point detection problem under a nontraditional false alarm probability constraint, which is desirable for a variety of applications. It is shown that in the multichart CUSUM test this constraint is easy to control. Furthermore, the proposed multichart CUSUM test is shown to be uniformly asymptotically optimal when the false alarm probability is small: it minimizes an average detection delay, or more generally, any positive moment of the stopping time distribution for any point of change.
Quickest change detection in distributed sensor systems
 Proc. 6th Intern. Conf. Inform. Fusion
, 2003
"... Abstract In the conventional formulation ofthe changepoint detection problem, there is a sequence ofobservations whose distribution changes at some unknown point in time, and the goal is to detect this change as quickly as possible, subject to false alarm constraints. It is known that in the case w ..."
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Cited by 29 (7 self)
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Abstract In the conventional formulation ofthe changepoint detection problem, there is a sequence ofobservations whose distribution changes at some unknown point in time, and the goal is to detect this change as quickly as possible, subject to false alarm constraints. It is known that in the case where the observations are independent and identically distributed (iid) and the change point is modeled as a geometrically distributed random variable, the Shiryaev detection procedure minimizes the expected detection delay, subject to a constraint on thefalse alarmpmbabilify In this paper; we present effective decentralized detection procedures for the multisensor situation where the information available for decisionmaking is distributed across a sef of sensors. We present asymptotically optimal procedures for two scenarios. In the prst scenario, fhe sensors send quantized versions of their observations to afusion center where the change detection is pedormed based on all the sensor messages. In the second scenario, the sensors perform local change detection using ShiryaPvRoberrs procedures and send theirfinal decisions to thefusion centerfor combining. We show that our decentralized pmcedures for latter scenario have the samefirst order asymptotic performance as the centralized ShiryaevRoberts procedure that has access to all of the sensor observations. We also present numerical results for a simple example involving Gaussian observations.
Performance of certain decentralized distributed change detection procedures
 Proceedings of the 9th International Conference on Information Fusion
"... Abstract – We compare several decentralized changepoint detection procedures for multisensor distributed systems when the information available for decisionmaking is distributed across a set of sensors. Asymptotically optimal procedures for two scenarios are presented. In the first scenario, the s ..."
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Cited by 21 (2 self)
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Abstract – We compare several decentralized changepoint detection procedures for multisensor distributed systems when the information available for decisionmaking is distributed across a set of sensors. Asymptotically optimal procedures for two scenarios are presented. In the first scenario, the sensors send quantized versions of their observations to a fusion center where change detection is performed based on all the sensor messages. If, in particular, the quantizers are binary, then the proposed binary CUSUM detection test is optimal in the class of tests with binary quantized data. In the second scenario, the sensors perform local change detection using the CUSUM procedures and send their final decisions to the fusion center for combining. The decision in favor of the change occurrence is made whenever CUSUM statistics at all sensors exceed thresholds. The latter decentralized procedure has the same first order asymptotic (as the false alarm rate is low) minimax operating characteristics as the globally optimal centralized detection procedure that has access to all the sensor observations. However, the presented Monte Carlo experiments for the Poisson example show that despite the fact that the procedure with local decisions is globally asymptotically optimal for a low false alarm rate, it performs worse than the procedure with binary quantization unless the false alarm rate is extremely low. In addition, two votingtype local decision based detection procedures are proposed and evaluated. Applications to network security (rapid detection of computer intrusions) are discussed.
Asymptotic Optimality Theory for Decentralized Sequential Hypothesis Testing in Sensor Networks
, 2002
"... The decentralized sequential hypothesis testing problem is studied in sensor networks, where a set of sensors receive independent observations and send summary messages to the fusion center, which makes a final decision. In the scenario where the sensors have full access to their past observations, ..."
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Cited by 20 (3 self)
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The decentralized sequential hypothesis testing problem is studied in sensor networks, where a set of sensors receive independent observations and send summary messages to the fusion center, which makes a final decision. In the scenario where the sensors have full access to their past observations, the first of asymptotically Bayes sequential tests is developed, and the proposed test has same asymptotic performance as the optimal centralized test that has access to all sensor observations. Next, in the scenario where the sensors do not have full access to their past observations, a simple but asymptotically Bayes sequential tests is developed, in which sensor message functions are what we call tandem quantizer, where each sensor only uses two different sensor quantizers with at most one switch between these two quantizers. Moreover, a new minimax formulation of finding optimal stationary sensor quantizers is proposed and is studied in detail in the case of additive Gaussian sensor noises. Finally, our results show that the feedback from the fusion center does not improve asymptotic performance in the scenario with full local memory, however, even a oneshot onebit feedback can significantly improve asymptotic performance in the scenario with limited local memory.
Asymptotically optimal quickest change detection in distributed sensor systems
 SEQUENTIAL ANALYSIS
, 2008
"... In the standard formulation of the quickest changepoint detection problem, a sequence of observations, whose distribution changes at some unknown point in time, is available to a decision maker, and the goal is to detect this change as quickly as possible, subject to false alarm constraints. In th ..."
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Cited by 20 (4 self)
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In the standard formulation of the quickest changepoint detection problem, a sequence of observations, whose distribution changes at some unknown point in time, is available to a decision maker, and the goal is to detect this change as quickly as possible, subject to false alarm constraints. In this paper, we study the quickest change detection problem in the setting where the information available for decisionmaking is distributed across a set of geographically separated sensors, and only a compressed version of observations in sensors may be used for final decisionmaking due to communication bandwidth constraints. We consider the minimax, uniform, and Bayesian versions of the optimization problem, and we present asymptotically optimal decentralized quickest change detection procedures for two scenarios. In the first scenario, the sensors send quantized versions of their observations to a fusion center where the change detection is performed based on all the sensor messages. In the second scenario, the sensors perform local change detection and send their final decisions to the fusion center for combining. We show that our decentralized procedures for the latter scenario have the same firstorder asymptotic performance as the corresponding centralized procedures that have access to all of the
Dataefficient quickest change detection with onoff observation control
 Sequential Analysis
, 2012
"... ..."
Objectbased change detection
 International Journal of Remote Sensing
, 2012
"... Abstract: Change detection has traditionally been seen as a centralized problem. Many change detection problems are however distributed in nature and the need for distributed change detection algorithms is therefore significant. In this paper a distributed change detection algorithm is proposed. The ..."
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Cited by 12 (3 self)
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Abstract: Change detection has traditionally been seen as a centralized problem. Many change detection problems are however distributed in nature and the need for distributed change detection algorithms is therefore significant. In this paper a distributed change detection algorithm is proposed. The change detection problem is first formulated as a convex optimization problem and then solved distributively with the alternating direction method of multipliers (ADMM). To further reduce the computational burden on each sensor, a homotopy solution is also derived. The proposed method have interesting connections with Lasso and compressed sensing and the theory developed for these methods are therefore directly applicable. 1.
Asymptotic optimality of changepoint detection schemes in general . . .
, 2006
"... In the early 1960s, Shiryaev obtained the structure of Bayesian stopping rules for detecting abrupt changes in independent and identically distributed sequences as well as in a constant drift of the Brownian motion. Since then, the methodology of optimal changepoint detection has concentrated on th ..."
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Cited by 11 (1 self)
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In the early 1960s, Shiryaev obtained the structure of Bayesian stopping rules for detecting abrupt changes in independent and identically distributed sequences as well as in a constant drift of the Brownian motion. Since then, the methodology of optimal changepoint detection has concentrated on the search for stopping rules that achieve the best balance of the mean detection delay and the rate of false alarms or minimize the mean delay under a fixed false alarm probability. In this respect, analysis of the performance of the Shiryaev procedure has been an open problem. Recently, Tartakovsky and Veeravalli (2005) investigated asymptotic performance of the Shiryaev Bayesian change detection procedure, the Page procedure, and the Shiryaev–Roberts procedure when the false alarm probability goes to zero for general discretetime models. In this article, we investigate the asymptotic performance of Shiryaev and Shiryaev–Roberts procedures for general continuoustime stochastic models for a small false alarm probability and small cost of detection delay. We show that the Shiryaev procedure has asymptotic optimality properties under mild conditions, while the Shiryaev–Roberts procedure may or may not be asymptotically optimal depending on the type of the prior distribution. The presented asymptotic Bayesian detection