Quickest Detection of the Poisson Disorder

Princeton University, Princeton NJ

Investigators

Abstract

In the simplest version of the Poisson disorder problem, the rate of a Poisson process changes at an unknown and unobservable time from one known constant to another, and the question is how to design a procedure that quickly detects the change-time. In this project, several new related problems, aligned more closely with real-life applications, are proposed: (1) Poisson disorder problems with intermediary inspections, (2) Poisson disorder problems with unknown post-disorder rate, and (3) quickest detection of the Poisson disorder given a fixed false-alarm rate. Other project goals are (4) to give a unified treatment of standard Poisson disorder problems, and (5) to develop computationally efficient and stable methods, still unavailable today, to calculate the parameters of quickest detection procedures. Solvable versions of the Poisson disorder problems typically reduce to an optimal stopping problem for a suitable jump process. However, most of the existing literature attacks the latter problem by using the general theory of optimal stopping for the processes with continuous sample-paths. This research recognizes the necessity of the special optimization methods for the jump processes. Particularly, sample-path techniques will be employed to meet the aforementioned project goals. The Poisson disorder problems manifest themselves naturally, for example, in the effective control and prevention of infectious diseases, quickest detection of quality and reliability problems in industrial processes, and surveillance of internet traffic to protect the network servers from "denial-of-service" attacks. This work is expected to produce new online quickest detection procedures that will enhance the efforts to maintain the welfare and the security of the nation. After remained open for nearly thirty years, Poisson disorder problems have recently started to receive satisfactory solutions. Hopefully, the direct approach of this project will continue to bring better insights into these problems, and in general, into the optimization problems for jump processes, lower the barriers to entry to these research areas and add to their momentums.