Minimax and pointwise sequential changepoint detection and identification for general stochastic models

TL;DR

This paper introduces a multihypothesis sequential detection and identification method for stochastic models, achieving asymptotic minimax and pointwise optimality in change detection tasks, including real-world COVID-19 detection.

Contribution

It proposes a novel multihypothesis change detection-identification procedure with proven asymptotic optimality for general stochastic models, including dependent observations.

Findings

Method controls false alarms and wrong identifications effectively.

Achieves faster COVID-19 detection compared to standard methods.

Applicable to multistream Markov ergodic processes.

Abstract

This paper considers the problem of joint change detection and identification assuming multiple composite postchange hypotheses. We propose a multihypothesis changepoint detection-identification procedure that controls the probabilities of false alarm and wrong identification. We show that the proposed procedure is asymptotically minimax and pointwise optimal, minimizing moments of the detection delay as probabilities of false alarm and wrong identification approach zero. The asymptotic optimality properties hold for general stochastic models with dependent observations. We illustrate general results for detection-identification of changes in multistream Markov ergodic processes. We consider several examples, including an application to rapid detection-identification of COVID-19 in Italy. Our proposed sequential algorithm allows much faster detection of COVID-19 than standard methods.