Minimax asymptotically optimal quickest change detection for statistically periodic data

Abstract

Theory and algorithms are developed for detecting changes in the distribution of statistically periodic random processes. The statistical periodicity is modeled using independent and periodically identically distributed processes, a new class of stochastic processes proposed by us. Algorithms are also developed for cases when the post-change distribution is not known or when there are multiple streams of observations. The algorithms are shown to be minimax asymptotically optimal as the mean time to the false alarm goes to infinity. The modeling is inspired by real datasets encountered in cyber–physical systems, biology, and medicine. The developed algorithms are applied to real and simulated data to verify their effectiveness in detecting changes.