Non-Parametric Quickest Detection of a Change in the Mean of an Observation Sequence

Abstract

We study the problem of quickest detection of a change in the mean of an observation sequence, under the assumption that both the pre- and post-change distributions have bounded support. We first study the case where the pre-change distribution is known, and then study the extension where only the mean and variance of the pre-change distribution are known. In both cases, no knowledge of the post-change distribution is assumed other than that it has bounded support. For the case where the pre-change distribution is known, we derive a test that asymptotically minimizes the worst-case detection delay over all post-change distributions, as the false alarm rate goes to zero. We then study the limiting form of the optimal test as the gap between the pre- and post-change means goes to zero, which we call the Mean-Change Test (MCT). We show that the MCT can be designed with only knowledge of the mean and variance of the pre-change distribution. We validate our analysis through numerical results for detecting a change in the mean of a beta distribution. We also demonstrate the use of the MCT for pandemic monitoring.