Change Acceleration and Detection

A generalization of the Bayesian sequential change detection problem is proposed, where the change is a latent event that should be not only detected, but also accelerated. It is assumed that the sequentially collected observations are responses to treatments selected in real time. The assigned treatments not only determine the distribution of responses before and after the change, but also influence when the change happens. The problem is to find a treatment assignment rule and a stopping rule to minimize the average total number of observations subject to a bound on the false-detection probability. An intuitive solution is proposed, which is easy to implement and achieves for a large class of change-point models the optimal performance up to a first-order asymptotic approximation. A simulation study suggests the almost exact optimality of the proposed scheme under a Markovian change-point model.