Numerical Comparison of Cusum and Shiryaev-Roberts Procedures for Detecting Changes in Distributions

TL;DR

This paper introduces a numerical method to systematically compare CUSUM and Shiryaev-Roberts procedures for change detection, revealing their performance differences in various scenarios, especially for small changes.

Contribution

A novel numerical approach for comparing change detection procedures, providing exact performance metrics and insights into their relative effectiveness.

Findings

Significant difference between procedures for small changes

Numerical method improves comparison accuracy

CUSUM optimal in minimax scenarios

Abstract

The CUSUM procedure is known to be optimal for detecting a change in distribution under a minimax scenario, whereas the Shiryaev-Roberts procedure is optimal for detecting a change that occurs at a distant time horizon. As a simpler alternative to the conventional Monte Carlo approach, we propose a numerical method for the systematic comparison of the two detection schemes in both settings, i.e., minimax and for detecting changes that occur in the distant future. Our goal is accomplished by deriving a set of exact integral equations for the performance metrics, which are then solved numerically. We present detailed numerical results for the problem of detecting a change in the mean of a Gaussian sequence, which show that the difference between the two procedures is significant only when detecting small changes.