Optimal detection of a change-set in a spatial Poisson process
Ivanoff, B. Gail ; Merzbach, Ely
Ann. Appl. Probab., Tome 20 (2010) no. 1, p. 640-659 / Harvested from Project Euclid
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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.
Publié le : 2010-04-15
Classification:  Sequential detection problem,  optimal stopping,  point process,  Poisson process,  stopping set,  change-set,  smooth semi-martingale,  likelihood function,  60G40,  60G55,  60G80 
@article{1268143435,
     author = {Ivanoff, B. Gail and Merzbach, Ely},
     title = {Optimal detection of a change-set in a spatial Poisson process},
     journal = {Ann. Appl. Probab.},
     volume = {20},
     number = {1},
     year = {2010},
     pages = { 640-659},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1268143435}
}

Ivanoff, B. Gail; Merzbach, Ely. Optimal detection of a change-set in a spatial Poisson process. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp.  640-659. http://gdmltest.u-ga.fr/item/1268143435/