Optimal Bayesian Quickest Detection for Hidden Markov Models and Structured Generalisations

In this paper we consider the problem of quickly detecting changes in hidden Markov models (HMMs) in a Bayesian setting, as well as several structured generalisations including changes in statistically periodic processes, quickest detection of a Markov process across a sensor array, quickest detection of a moving target in a sensor network and quickest change detection (QCD) in multistream data. Our main result establishes an optimal Bayesian HMM QCD rule with a threshold structure. This framework and proof techniques allow us to to elegantly establish optimal rules for several structured generalisations by showing that these problems are special cases of the Bayesian HMM QCD problem. We develop bounds to characterise the performance of our optimal rule and provide an efficient method for computing the test statistic. Finally, we examine the performance of our rule in several simulation examples and propose a technique for calculating the optimal threshold

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

In this paper 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