Optimal detection of a change-set in a spatial Poisson process

TL;DR

This paper extends change-point detection to a spatial setting, proposing optimal methods for identifying unobservable change-sets in a Poisson process using martingale techniques, with practical examples.

Contribution

It introduces a new change-set detection framework for spatial Poisson processes and provides sufficient conditions for optimal detection using advanced probabilistic methods.

Findings

Established a sufficient condition for optimal detection of change-sets.

Applied martingale techniques to the change-set detection problem.

Discussed practical examples illustrating the method.

Abstract

We generalize the classic change-point problem to a "change-set" framework: a spatial Poisson process changes its intensity on an unobservable random set. Optimal detection of the set is defined by maximizing the expected value of a gain function. In the case that the unknown change-set is defined by a locally finite set of incomparable points, we present a sufficient condition for optimal detection of the set using multiparameter martingale techniques. Two examples are discussed.