Quickest Change Detection with Non-Stationary Post-Change Observations

TL;DR

This paper addresses quickest change detection when post-change observations are non-stationary with parametric uncertainty, proposing asymptotically optimal procedures and validating them through simulations and pandemic monitoring applications.

Contribution

It introduces a universal lower bound on detection delay and develops window-limited CuSum and GLR-CuSum procedures that achieve this bound under non-stationary post-change conditions.

Findings

The proposed procedures are asymptotically optimal as false alarm rate approaches zero.

Numerical results confirm the effectiveness of the methods on synthetic data.

Application to pandemic monitoring demonstrates practical utility.

Abstract

The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. The pre-change observations are assumed to be stationary with a known distribution, while the post-change observations are allowed to be non-stationary with some possible parametric uncertainty in their distribution. In particular, it is assumed that the cumulative Kullback-Leibler divergence between the post-change and the pre-change distributions grows in a certain manner with time after the change-point. For the case where the post-change distributions are known, a universal asymptotic lower bound on the delay is derived, as the false alarm rate goes to zero. Furthermore, a window-limited Cumulative Sum (CuSum) procedure is developed, and shown to achieve the lower bound asymptotically. For the case where the post-change distributions have parametric uncertainty, a window-limited (WL) generalized likelihood-ratio (GLR) CuSum procedure is developed and is shown to achieve the universal lower bound asymptotically. Extensions to the case with dependent observations are discussed. The analysis is validated through numerical results on synthetic data. The use of the WL-GLR-CuSum procedure in monitoring pandemics is also demonstrated.