Sequential Change Diagnosis Revisited and the Adaptive Matrix CuSum

TL;DR

This paper revisits the problem of sequential change diagnosis, proposing a new recursive algorithm that improves detection accuracy without extra tuning, supported by theoretical analysis and extensive simulations.

Contribution

A novel recursive algorithm for sequential change diagnosis that avoids implicit use of pre-change data and enhances detection accuracy without additional parameters.

Findings

The proposed algorithm effectively reduces misidentification probabilities.

Theoretical analysis supports the algorithm's optimality in Lorden's sense.

Simulation studies demonstrate superior performance over existing methods.

Abstract

The problem of sequential change diagnosis is considered, where observations are obtained on-line, an abrupt change occurs in their distribution, and the goal is to quickly detect the change and accurately identify the post-change distribution, while controlling the false alarm rate. A finite set of alternatives is postulated for the post-change regime, but no prior information is assumed for the unknown change-point. A drawback of many algorithms that have been proposed for this problem is the implicit use of pre-change data for determining the post-change distribution. This can lead to very large conditional probabilities of misidentification, given that there was no false alarm, unless the change occurs soon after monitoring begins. A novel, recursive algorithm is proposed and shown to resolve this issue without the use of additional tuning parameters and without sacrificing control of the worst-case delay in Lorden's sense. A theoretical analysis is conducted for a general family of sequential change diagnosis procedures, which supports the proposed algorithm and revises certain state-of-the-art results. Additionally, a novel, comprehensive method is proposed for the design and evaluation of sequential change diagnosis algorithms. This method is illustrated with simulation studies, where existing procedures are compared to the proposed.