An Asymptotic Theory of Joint Sequential Changepoint Detection and Identification for General Stochastic Models

TL;DR

This paper develops an asymptotic theory for joint sequential changepoint detection and identification in complex stochastic models, extending previous work to multiple hypotheses with nearly optimal performance.

Contribution

It introduces a multi-hypothesis detection-identification rule that generalizes existing theory to dependent, non-i.i.d. data with composite post-change hypotheses.

Findings

The proposed rule is nearly optimal in minimizing detection delay.

The theory applies to dependent and non-i.i.d. data.

It handles multiple composite post-change hypotheses.

Abstract

The paper addresses a joint sequential changepoint detection and identification/isolation problem for a general stochastic model, assuming that the observed data may be dependent and non-identically distributed, the prior distribution of the change point is arbitrary, and the post-change hypotheses are composite. The developed detection-identification theory generalizes the changepoint detection theory developed by Tartakovsky (2019) to the case of multiple composite post-change hypotheses when one has not only to detect a change as quickly as possible but also to identify (or isolate) the true post-change distribution. We propose a multi-hypothesis change detection-identification rule and show that it is nearly optimal, minimizing moments of the delay to detection as the probability of a false alarm and the probabilities of misidentification go to zero.