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.
Citation
B. Gail Ivanoff. Ely Merzbach. "Optimal detection of a change-set in a spatial Poisson process." Ann. Appl. Probab. 20 (2) 640 - 659, April 2010. https://doi.org/10.1214/09-AAP629
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