Quickest Search for a Change Point

TL;DR

This paper develops an optimal sequential detection method for identifying the earliest transient change point in a data sequence, balancing quick detection with false alarm control, and proves its optimality in a minimax setting.

Contribution

It introduces a Shewhart test-based approach for quickest change-point detection that is proven to be optimal in a minimax framework with transient changes, extending traditional methods.

Findings

Shewhart test achieves exact optimality for quickest change detection.

The method effectively balances detection speed and false alarm rate.

Numerical results confirm the theoretical optimality and practical performance.

Abstract

This paper considers a sequence of random variables generated according to a common distribution. The distribution might undergo periods of transient changes at an unknown set of time instants, referred to as change-points. The objective is to sequentially collect measurements from the sequence and design a dynamic decision rule for the quickest identification of one change-point in real time, while, in parallel, the rate of false alarms is controlled. This setting is different from the conventional change-point detection settings in which there exists at most one change-point that can be either persistent or transient. The problem is considered under the minimax setting with a constraint on the false alarm rate before the first change occurs. It is proved that the Shewhart test achieves exact optimality under worst-case change points and also worst-case data realization. Numerical evaluations are also provided to assess the performance of the decision rule characterized.