Bayesian Quickest Detection of Changes in Statistically Periodic Processes

Bayesian optimality theory is developed for quickest change detection in a class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes. This class of processes can be used to model periodically varying statistical behavior. An algorithm called the periodic-Shiryaev algorithm is proposed and is shown to asymptotically minimize the average detection delay subject to a constraint on the probability of false alarm. It is also shown that the statistic for this algorithm can be computed recursively and using a finite amount of memory. This problem has applications in anomaly detection problems in cyber-physical systems and biology, where periodic statistical behavior has been observed.