Bayesian Two-Stage Sequential Change Diagnosis Via Multi-Sensor Array

Abstract

In this paper, we formulate and solve a two-stage Bayesian sequential change diagnosis (SCD) problem in a multi-sensor setting. In the considered problem, the change propagates across the sensor array gradually. After a change is detected, we are allowed to continue observing more samples so that we can identify the distribution after the change more accurately. The goal is to minimize the total cost including delay, false alarm, and misdiagnosis probabilities. We characterize the optimal SCD rule. Moreover, to address the high computational complexity issue of the optimal SCD rule, we propose a low-complexity threshold rule that is asymptotically optimal as the unit delay costs go to zero.