Sequential Detection of Transient Signals with Exponential Family Distribution

TL;DR

This paper extends sequential detection methods for transient signals within exponential family distributions, analyzing false detection probabilities and detection power, and introduces a generalized likelihood ratio chart that outperforms traditional methods in various scenarios.

Contribution

It generalizes the moving average chart to exponential families and develops a generalized signed likelihood ratio chart for detecting transient parameter changes.

Findings

The generalized signed likelihood ratio chart performs well compared to CUSUM and S-R procedures.

The methods effectively detect mean or variance changes in normal models.

Illustrations include real-world examples demonstrating practical utility.

Abstract

We first consider the sequential detection of transient signals by generalizing the moving average chart to exponential family and study the false detection probability (FDP) and power of detection (POD) in the steady state. Then windowed adjusted signed (or modified directed) likelihood ratio chart is studied by treating it as normal random variable. In the multi-parameter exponential family, the detection of the transient change of one of the canonical parameters or a function of canonical parameters is considered by using the generalized adjusted signed likelihood ratio chart. Comparisons with window restricted CUSUM and Shiryayev-Roberts (S-R) procedures show that the generalized signed likelihood ratio chart performs quite well. Several important examples including the mean or variance change under normal model and a real example are used for illustration.