Bayesian Change Detection

In this thesis we consider certain problems of optimal change detection in which the task is to decide in a sequential manner which of two probabilitic system descriptions account for given, observed data. Optimal decisions are defined acccording to an average cost criterion which has a penalty which increases with time and a penalty for incorrect decisions. We consider observation processes of both the diffusion and point process kind. A main result is a verfication-type theorem which permits one to prove the optimality of candidate decision policies provided one can find a certain function and interval. The form of the theorem suggests how to go about looking for such a pair. As applications we consider the sequential detection and disruption problems involving diffusion observations and give new proofs of existence of the optimal thresholds as well as a new, simple algorithm for their computation. In the case of sequential detection between Poisson processes we solve the so-called overshoot problem exactly for the first time using the same algorithm.