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

B. Gail Ivanoff · Ely Merzbach

10 citations0/0 files storedThe Annals of Applied Probability

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Advanced Statistical Process Monitoring Probability and Statistical Research Point processes and geometric inequalities

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.

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1994Change-point problems 2002Solving the Poisson Disorder Problem 2004Optimal Detection of a Change Point in a Poisson Process for Different Observation Schemes

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2015Robustness of the N-CUSUM stopping rule in a Wiener disorder problem

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