Bayesian Quickest Transient Change Detection

We consider the problem of quickest transient change detection under a Bayesian setting. The change occurs at a random time Γ1 and disappears at a random time Γ2 > Γ1. Thus, at any time k, the system can be in one of the following states, i) prechange, ii) in–change, and iii) out–of–change. We model the evolution of the state by a Markov chain. The state of the system can only be observed partially from the observations which are obtained sequentially. We formulate the quickest transient change detection problem as a Partially Observable Markov Decision Process (POMDP) and obtain the following detection rules for a target probability of false alarm PFA 6 α, 1. MinD (Minimum Detection Delay), which minimizes the mean detection delay EDD 2. A–MinD (Asymptotic Minimum Detection Delay), which is an asymptotic version of the procedure MinD when the mean time until the occurrence of change, E ˆ