Bayesian Quickest Detection of Propagating Spatial Events

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 multi-sensor 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 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, and specific analysis is conducted in the setting of detecting attenuating random signals. Then, we show how the proposed procedure is easy to extend for detecting multiple propagating spatial events in parallel. A method that provides false discovery rate (FDR) control is proposed. In the simulation section, it is clearly demonstrated that exploiting the spatial properties of the event decreases the ADD compared to procedures that do not utilize this information, even under model mismatch.