Exactly optimal Bayesian quickest change detection for general dependent processes

This paper considers the quickest detection problem for general dependent processes in a Bayesian setting. This paper establishes that Shiryaev’s rule, a simple threshold test on the no-change posterior, is an exactly optimal solution in the general dependent setting when the change time prior distribution is geometric. The presented analysis approach provides insights into the necessity and sufficiency of the change time prior distribution assumption and highlights how the nature of optimal solutions will change under assumption relaxation. This paper also establishes that strong duality holds when measurements have continuous conditional distributions. Finally, a novel, computationally efficient, relaxed-dependence test statistic is proposed which is shown to be weakly convergent to Shiryaev’s test statistic.