Area-interaction point processes

Adrian Baddeley, M.N.M. Van Lieshout

    Research output: Contribution to journalArticle

    120 Citations (Scopus)

    Abstract

    We introduce a new Markov point process that exhibits a range of clustered, random, and ordered patterns according to the value of a scalar parameter. In contrast to pairwise interaction processes, this model has interaction terms of all orders. The likelihood is closely related to the empty space function F, paralleling the relation between the Strauss process and Ripley's K-function. We show that, in complete analogy with pairwise interaction processes, the pseudolikelihood equations for this model are a special case of the Takacs-Fiksel method, and our model is the limit of a sequence of auto-logistic lattice processes.
    Original languageEnglish
    Pages (from-to)601-619
    JournalAnnals of the Institute of Statistical Mathematics
    Volume47
    DOIs
    Publication statusPublished - 1995

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