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

B. Gail Ivanoff, Ely Merzbach

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish
Pages (from-to)640-659
Number of pages20
JournalAnnals of Applied Probability
Issue number2
StatePublished - Apr 2010


  • Change-set
  • Likelihood function
  • Optimal stopping
  • Point process
  • Poisson process
  • Sequential detection problem
  • Smooth semi-martingale
  • Stopping set


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