(20110221) Multi-dimensional quickest detection - Ομιλία Ολυμπίας Χατζηλιάδη, Athens

Την ερχόμενη Δευτέρα 21/02/11 στις 12μ θα δώσει ομιλία η Ολυμπία Χατζηλιάδη, Associate Professor of Mathematics, Department of Mathematics at Brooklyn College and the Graduate Center of the City
University of New York.
Πληροφορίες σχετικά με την ομιλία θα βρείτε στο τέλος του email.

Τα σεμινάρια του τομέα μας πραγματοποιούνται στην αίθουσα Α32, κτήριο Μαθηματικού τμήματος, 2ος όροφος.

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Φώτης Σιάννης
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Title: Multi-dimensional quickest detection

Abstract:

We consider the problem of quickest detection in the presence of multiple random sources each driven by distinct sources of noise represented by a Brownian motion. We make the assumption that thedriving noises are independent. We identify the problem of two-sided alternatives as a special case of this problem in the case that the driving Brownian motions have a correlation equal to -1. The case described in this set-up corresponds to 0 correlation in the noise component of each source. The first problem we will address is the one of detecting a change in the drift of Brownian motions received in parallel at the sensors of decentralized systems. We examine the performance of one shot schemes in decentralized detection in the case of many sensors with respect to appropriate criteria. One shot schemes are schemes in which the sensors communicate with the fusion center only once; when they must signal a detection. The communication is clearly asynchronous and we consider the case that the fusion center employs one of two strategies, the minimal and the maximal. According to the former strategy an alarm is issued at the fusion center the moment in which the first one of the sensors issues an alarm, whereas according to the latter strategy an alarm is issued when both sensors have reported a detection. In this work we derive closed form expressions for the expected delay of both the minimal and the maximal strategies in the case that CUSUM stopping rules are employed by the sensors. We prove asymptotic optimality of the above strategies in the case of across-sensor independence and specify the optimal threshold selection at the sensors.

Moreover, we consider the problem of quickest detection of signals in a coupled system of N sensors, which receive continuous sequential observations from the environment. It is assumed that the signals, which are modeled by a general Itȏ processes, are coupled across sensors, but that their onset times may differ from sensor to sensor. Two main cases are considered; in the first one signal strengths are the same across sensors while in the second one they differ by a constant. The objective is the optimal detection of the first time at which any sensor in the system receives a signal. The problem is formulated as a stochastic optimization problem in which an extended minimal Kullback-Leibler divergence criterion is used as a measure of detection delay, with a constraint onthe mean time to the first false alarm. The case in which the sensors employ cumulative sum (CUSUM) strategies is considered, and it is proved that the minimum of N CUSUMs is asymptotically optimal as the mean time between false alarms increases without bound. In particular, in the case of equal signal strengths across sensors, it is seen that the difference in detection delay of the N-CUSUM stopping rule and the unknown optimal stopping scheme tends to a constant related to the number of sensors as the mean time between false alarms increases without bound. While in the case of unequal signal strengths, it is seen that this difference tends to 0.