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

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

2010-09-28

arxiv.org/abs/1009.5748v1

Annals of Applied Probability 2010, Vol. 20, No. 2, 640-659

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP629 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP629

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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