Quickest change detection under transient dynamics

Abstract

The problem of transient quickest change detection (QCD) is studied, in which the change from the initial to the final phase does not happen instantaneously, but after a series of cascading transient phases of finite durations, each one corresponding to a different probability distribution. The goal is to design a stopping rule to detect the change as quickly as possible, subject to false alarm constraints. In previous work, the D-CuSum algorithm was proposed for such a QCD problem. The D-CuSum does not incorporate any prior statistical information about the durations of the transient periods. In this work, we develop an algorithm, the D-S-R algorithm, which incorporates geometric priors on the durations of the transient periods. We compare the D-CuSum and D-S-R algorithms in numerical examples to develop some insights about the role of the prior on the transient durations on the performance.