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arXiv · 1009.5748

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

B. Gail Ivanoff·Ely Merzbach
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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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B. Gail Ivanoff, Ely Merzbach. 2010-09-28. Optimal detection of a change-set in a spatial Poisson process. https://doi.org/10.1214/09-aap629

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