Exactly Optimal Quickest Change Detection of Markov Chains

This letter establishes that an exactly optimal rule for Bayesian Quickest Change Detection (QCD) of Markov chains is an optimal stopping rule in the form of a threshold test on the no change posterior. We also provide a computationally efficient scalar filter for the no change posterior whose effort is independent of the dimension of the chains. We establish that an (undesirable) weak practical super-martingale phenomenon can be exhibited by the no change posterior when the before and after chains are too close in a relative entropy rate sense. The proposed detector is examined in simulation studies.