Open Access
April 2010 Optimal detection of a change-set in a spatial Poisson process
B. Gail Ivanoff, Ely Merzbach
Ann. Appl. Probab. 20(2): 640-659 (April 2010). DOI: 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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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.


Published: April 2010
First available in Project Euclid: 9 March 2010

zbMATH: 1213.62130
MathSciNet: MR2650044
Digital Object Identifier: 10.1214/09-AAP629

Primary: 60G40 , 60G55
Secondary: 60G80

Keywords: change-set , likelihood function , Optimal stopping , point process , Poisson process , Sequential detection problem , smooth semi-martingale , stopping set

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.20 • No. 2 • April 2010
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