  Rapid detection of spatial events that propagate across a sensor network is
of wide interest in many modern applications. In particular, in communications,
radar, IoT, environmental monitoring, and biosurveillance, we may observe
propagating fields or particles. In this paper, we propose Bayesian sequential
single and multiple change-point detection procedures for the rapid detection
of such phenomena. Using a dynamic programming framework we derive the
structure of the optimal single-event quickest detection procedure, which
minimizes the average detection delay (ADD) subject to a false alarm
probability upper bound. The multi-sensor system configuration is arbitrary and
sensors may be mobile. 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 characteristics 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 random Gaussian signals affected by path loss. Then, we show how the
proposed procedure is easy to extend for detecting multiple propagating spatial
events in parallel in a multiple hypothesis testing setting. A method that
provides strict false discovery rate (FDR) control is proposed. In the
simulation section, it is 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.
