Prof. George Moustakides (University of Patras, Greece)

Title: Sequential rate change detection in Poisson processes

Abstract: We consider the Cumulative Sum (CUSUM) test as a possible candidate for sequential detection of an abrupt change in the rate of a homogeneous Poisson process. We first derive a closed form expression for the average run length of the CUSUM stopping time, which we use to prove optimality of the CUSUM test in the sense of Lorden. Specifically, we demonstrate that the CUSUM stopping time minimizes the maximal possible conditional detection delay under the constraint that the average period between false alarms is no less than a prescribed value. We then consider a special category of rate changes in non-homogeneous Poisson processes and we show that the optimality of CUSUM extends to this more general class, provided that we suitably modify our initial performance measure. We conclude our presentation by discussing the applicability of the non-homegeneous Poisson detection problem to Epidemic surveillance.