The Annals of Applied Probability

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

B. Gail Ivanoff and Ely Merzbach

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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.

Article information

Ann. Appl. Probab., Volume 20, Number 2 (2010), 640-659.

First available in Project Euclid: 9 March 2010

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Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G55: Point processes
Secondary: 60G80

Sequential detection problem optimal stopping point process Poisson process stopping set change-set smooth semi-martingale likelihood function


Ivanoff, B. Gail; Merzbach, Ely. Optimal detection of a change-set in a spatial Poisson process. Ann. Appl. Probab. 20 (2010), no. 2, 640--659. doi:10.1214/09-AAP629.

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