An Optimal Retrospective Change Point Detection Policy

.  Since the middle of the twentieth century, the problem of making inferences about the point in a surveyed series of observations at which the underlying distribution changes has been extensively addressed in the economics, biostatistics and statistics literature. Cumulative sum‐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 most powerful testing.