ISyE Seminar - Alexander Tartakovsky
TITLE: Nearly Optimal Multistream Sequential Tests: The Non-i.i.d. Case
We consider the problem of sequential signal detection in a multistream setup assuming that there is a multichannel system where the number and location of signals (if any) is a priori unknown. We suppose that the data in each stream/channel follow a very general non-i.i.d. stochastic model. Under the assumption that the local log-likelihood ratio processes in the channels converge r-completely to positive and finite numbers, we establish the asymptotic optimality property of a generalized sequential likelihood ratio test and a mixture-based sequential likelihood ratio test. Specifically, we show that both tests minimize the first r moments of the stopping time distribution asymptotically as the probabilities of false alarm and missed detection approach zero. The general detection theory is illustrated by several practical examples. Finally, we discuss the feasibility of both sequential tests in terms of computational complexity and compare their non-asymptotic performance in a simulation study. This is joint work with Georgios Fellouris.