Bayesian Method for Spatial Change-Point Detection of Propagating Event
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Rapid detection of spatial events that propagate across a sensor network is of wide interest in many modern applications. In particular, in communications, radar, environmental monitoring, and biosurveillance, we may observe propagating fields or particles. In this paper, we propose Bayesian single and multiple change-point detection procedures for the rapid detection of propagating spatial events. It is assumed that the spatial event propagates across a network of sensors according to the physical properties of the source causing the event. The multisensor system configuration is arbitrary and sensors may be mobile. We begin by considering a single spatial event and are interested in detecting this event as quickly as possible, while statistically controlling the probability of false alarm. Using a dynamic programming framework we derive the structure of the optimal procedure, which minimizes the average detection delay (ADD) subject to a false alarm probability upper bound. In the rare event regime, the optimal procedure converges to a more practical threshold test on the posterior probability of the change point. A convenient recursive computation of this posterior probability is derived by using the propagation pattern of the spatial event. The ADD of the posterior probability threshold test is analyzed in the asymptotic regime. Then, we take a multiple hypothesis testing (MHT) approach and develop a procedure for the detection of multiple propagating spatial events in parallel. The proposed parallel procedure controls the overall false discovery rate (FDR) under prespecified upper bound. Simulations are conducted to verify the theoretical findings. It is shown that exploiting the spatial properties of the event improves the ADD compared to procedures that do not properly take advantage of the spatial information.
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