Exactly Optimal Bayesian Quickest Change Detection for Hidden Markov Models

This paper considers the quickest detection problem for hidden Markov models (HMMs) in a Bayesian setting. We construct an augmented HMM representation of the problem that allows the application of a dynamic programming approach to prove that Shiryaev's rule is an (exact) optimal solution. This augmented representation highlights the problem's fundamental information structure and suggests possible relaxations to more exotic change event priors not appearing in the literature. Finally, this augmented representation also allows us to present an efficient computational method for implementing the optimal solution.