Quickest change detection with unknown post-change distribution

Abstract

This paper considers the problem of quickest detection of a change in distribution under the assumption that the pre-change distribution π is known, and the post-change distribution μ is unknown and belongs to a general class of distributions. Using the knowledge of the pre-change distribution π, the sample space is partitioned into equiprobable intervals and the number of samples falling into each of these intervals is monitored to detect the change. A test statistic that approximates the generalized likelihood ratio test is proposed. A recursive update scheme to compute the statistic efficiently and an approximation of the average run-length to false alarm are also derived. Simulations show that our approach is comparable in performance to two other non-parametric quickest change detection methods if the change is either a shift in distribution mean or variance, respectively. But our method significantly outperforms them if these distribution change assumptions are violated.