Multi-Chart Detection Procedure for Bayesian Quickest Change-Point Detection with Unknown Post-Change Parameters

TL;DR

This paper introduces multi-chart detection procedures for Bayesian quickest change-point detection with unknown post-change parameters, achieving asymptotic optimality and efficient recursive computation, even in multi-source scenarios.

Contribution

It proposes novel multi-chart detection algorithms that handle uncertainty in post-change parameters and extend to multi-source monitoring with linear complexity.

Findings

Asymptotic optimality for finite post-change parameter sets

Efficient recursive computation of detection statistics

Linear complexity in multi-source monitoring

Abstract

In this paper, the problem of quickly detecting an abrupt change on a stochastic process under Bayesian framework is considered. Different from the classic Bayesian quickest change-point detection problem, this paper considers the case where there is uncertainty about the post-change distribution. Specifically, the observer only knows that the post-change distribution belongs to a parametric distribution family but he does not know the true value of the post-change parameter. In this scenario, we propose two multi-chart detection procedures, termed as M-SR procedure and modified M-SR procedure respectively, and show that these two procedures are asymptotically optimal when the post-change parameter belongs to a finite set and are asymptotically $\epsilon-$optimal when the post-change parameter belongs to a compact set with finite measure. Both algorithms can be calculated efficiently as their detection statistics can be updated recursively. We then extend the study to consider the multi-source monitoring problem with unknown post-change parameters. When those monitored sources are mutually independent, we propose a window-based modified M-SR detection procedure and show that the proposed detection method is first-order asymptotically optimal when post-change parameters belong to finite sets. We show that both computation and space complexities of the proposed algorithm increase only linearly with respect to the number of sources.