Optimal Two-Stage Bayesian Sequential Change Diagnosis

In this paper, we formulate and solve a two-stage Bayesian sequential change diagnosis problem. Different from the one-stage sequential change diagnosis problem considered in the existing work, after a change has been detected, we can continue to collect samples so that we can identify the distribution after change more accurately. The goal is to minimize the total cost including delay, false alarm and mis-diagnosis probabilities. We first convert the two-stage sequential change diagnosis problem into a two-ordered optimal stopping time problem. Using tools from multiple optimal stopping time problems, we obtain the optimal change detection and distribution identification rules.