Optimal detection of the support of a Poisson process

Abstract

We address the problem of the optimal detection of the support of a Poisson process in one and two dimensions. The point process N is assumed to be distributed according to a Poisson process with intensity mu on an unobservable random set xi. In one dimension, xi = [sigma, infinity) where sigma is a change-point. In two dimensions, the boundary of xi is determined by one or more incomparable points. The goal is to detect xi in an optimal way by maximizing the expected value of a reward function. Optimal solutions are found in the one dimensional case for two different information schemes. Analytical and practical approaches are provided in the two dimensional case.