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Area-interaction point processes

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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 functionF, paralleling the relation between the Strauss process and Ripley'sK-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.

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Authors and Affiliations

  1. Department of Mathematics, University of Western Australia, 6009, Nedlands, WA, Australia

    A. J. Baddeley

  2. Department of Mathematics and Computer Science, University of Leiden, The Netherlands

    A. J. Baddeley

  3. Department of Statistics, University of Warwick, CV4 7AL, Coventry, UK

    M. N. M. van Lieshout

Authors
  1. A. J. Baddeley
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  2. M. N. M. van Lieshout
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Baddeley, A.J., van Lieshout, M.N.M. Area-interaction point processes. Ann Inst Stat Math 47, 601–619 (1995). https://doi.org/10.1007/BF01856536

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