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SUMMARY:Multi-Dimensional Quickest Detection
DESCRIPTION:ABSTRACT
In this talk, I will discuss the problem of quickest detection in the presence of multiple, correlated, random sources driven by distinct noise origins represented by a Brownian motion.
The first issue is detecting a change in the drift of independent Brownian motions received in parallel at the sensors of decentralized systems. I will examine the performance of one-shot schemes in decentralized detection in the case of many sensors, with respect to appropriate criteria. In one-shot schemes, the sensors communicate with the fusion center only once: to signal a detection. That communication is clearly asynchronous. I consider the case in which the fusion center employs the minimal strategy, namely issuing an alarm the moment it receives the first sensor detection. I hope to prove asymptotic optimality of the above strategy not only in the case of independent sources of data but also in the presence of across-sensor correlations and specify the optimal threshold selection at the sensors.
Second, I will 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 process, are coupled across sensors, but that their onset times may differ from sensor to sensor. I will discuss two cases: the first assumes signal strengths are the same across sensors the second case assumes the signals 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 on the 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-CUSUM 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. In the case of unequal signal strengths, it is seen that this difference is asymptotic to zero.
BIOGRAPHY
Olympia Hadjiliadis studied statistics in Toronto and mathematics with specialization in finance at the University of Waterloo, Canada. She received her Ph.D. from the Department of Statistics at Columbia University. Prior to her current position at Hunter College, City University of New York, Hadjiliadis was a postdoctoral fellow in the Department of Electrical Engineering at Princeton University.
Her research interests are in the areas of quickest detection and sequential analysis, computer vision and finance.
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