An optimal retrospective change point detection policy

ABSTRACT. Since the middle of the twentieth century, the problem of making infer-ences about the point in a surveyed series of observations at which the underlying distri-bution changes has been extensively addressed in the economics, biostatistics and statis-tics literature. CUSUM type statistics have commonly been thought to play a central role in non-sequential change point detections. Alternatively, we present and examine an approach based on the Shiryayev-Roberts scheme. We show that retrospective change point detection policies based on Shiryayev-Roberts statistics are non-asymptotically optimal in the context of the most powerful testing. Key words: bayes factors, change point, CUSUM, likelihood, mixture type testing, most powerful testing, optimality, Shiryayev-Roberts