  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.
