A Framework for Bayesian Quickest Change Detection in General Dependent Stochastic Processes

Abstract

In this letter we present a novel framework for quickly detecting a change in a general dependent stochastic process. We propose that any general dependent Bayesian quickest change detection (QCD) problem can be converted into a hidden Markov model (HMM) QCD problem, provided that a suitable state process can be constructed. The optimal rule for HMM QCD is then a simple threshold test on the posterior probability of a change. We investigate case studies that can be considered structured generalisations of Bayesian HMM QCD problems including: quickly detecting changes in statistically periodic processes and quickest detection of a moving target in a sensor network. Using our framework we pose and establish the optimal rules for these case studies. We also illustrate the performance of our optimal rule on real air traffic data to verify its simplicity and effectiveness in detecting changes.