A0816
Title: Two-stage sequential change diagnosis problems
Authors: Lifeng Lai - University of California, Davis (United States) [presenting]
Abstract: A two-stage Bayesian sequential change diagnosis (SCD) problem is formulated and solved. In the SCD problem, after a change is detected, one also needs to determine what the post-change distribution is. Different from the one-stage sequential change diagnosis problem considered in the existing work, after a change has been detected, it is possible to continue collecting low-cost samples so that the post-change distribution can be identified more accurately. The goal of a two-stage SCD rule is to minimize the total cost, including delay, false alarm probability, and misdiagnosis probability. To solve the two-stage SCD problem, the problem is first converted into a two-ordered optimal stopping time problem. Using tools from optimal multiple stopping time theory, the optimal SCD rule is obtained. Moreover, to address the high computational complexity issue of the optimal SCD rule, a computationally efficient threshold-based two-stage SCD rule is further proposed. By analyzing the asymptotic behaviors of the delay, false alarm, and misdiagnosis costs, it is shown that the proposed threshold SCD rule is asymptotically optimal as the per-unit delay costs go to zero.
