Bayesian Quickest Detection of Propagating Spatial Events

TL;DR

This paper develops Bayesian sequential detection methods for rapidly identifying propagating spatial events across sensor networks, optimizing detection delay while controlling false alarms, and extends to multiple events with FDR control.

Contribution

It introduces a Bayesian framework for quickest detection of propagating spatial events, deriving optimal procedures, recursive computation methods, and extensions to multiple events with FDR control.

Findings

Optimal detection delay converges to a threshold test in the rare event regime.

Exploiting spatial properties reduces detection delay compared to non-spatial methods.

Proposed methods perform well even under model mismatch.

Abstract

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.