On Insufficiently Informative Measurements in Bayesian Quickest Change Detection and Identification

In this paper, we describe an undesirable weak practical super-martingale hallucination phenomenon that can emerge in the Bayesian quickest detection and identification problem. We establish that when measurements are insufficiently informative, a situation described by a relative entropy condition on measurement densities, the Bayesian quickest detection and identification solution can (undesirably) become increasingly confident that a change has occurred, even when it has not. Finally, we illustrate the phenomenon in simulation studies and the vision-based aircraft detection application which illustrates the optimal rule can be unsuitable in the sense of hallucinating a change that has not occurred.