Asymptotic Minimax Robust Quickest Change Detection for Dependent Stochastic Processes with Parametric Uncertainty

Abstract

In this paper, we consider the problem of quickly detecting an unknown change in the conditional densities of a dependent stochastic process. In contrast to the existing quickest change detection approaches for dependent stochastic processes, we propose minimax robust versions of the popular Lorden, Pollak, and Bayesian criteria for when there is uncertainty about the parameter of the post-change conditional densities. Under an information-theoretic Pythagorean inequality condition on the uncertainty set of possible post-change parameters, we identify asymptotic minimax robust solutions to our Lorden, Pollak, and Bayesian problems. Finally, through simulation examples, we illustrate that asymptotically minimax robust rules can provide detection performance comparable to the popular (but more computationally expensive) generalized likelihood ratio rule.