OPTIMAL DETECTION OF A CHANGE-SET IN A SPATIAL POISSON PROCESS

• 成果类型: Article
• 署名作者: Ivanoff, B. Gail; Merzbach, Ely
• 署名单位: University of Ottawa; Bar Ilan University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP629
• 发表日期: 2010
• 页码: 640-659
• 关键词: point

摘要

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.