Sequential change detection revisited

TL;DR

This paper introduces a unified framework for sequential change detection that models the change point as a random time, enabling better understanding and comparison of existing criteria, and proposes new performance measures with optimal detection strategies.

Contribution

It presents a general modeling framework for change detection criteria and derives optimal detection procedures for a new criterion extending Lorden's measure.

Findings

Unified framework captures most known criteria

Derived optimal detection for the new criterion

Provides formulas for optimal performance in Brownian motion cases

Abstract

In sequential change detection, existing performance measures differ significantly in the way they treat the time of change. By modeling this quantity as a random time, we introduce a general framework capable of capturing and better understanding most well-known criteria and also propose new ones. For a specific new criterion that constitutes an extension to Lorden's performance measure, we offer the optimum structure for detecting a change in the constant drift of a Brownian motion and a formula for the corresponding optimum performance.