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Likelihood Inference for Gibbs Processes in the Analysis of Spatial Point Patterns

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  • Jorge Mateu
  • Francisco Montes

Abstract

Several authors have proposed stochastic and non‐stochastic approximations to the maximum likelihood estimate (MLE) for Gibbs point processes in modelling spatial point patterns with pairwise interactions. The approximations are necessary because of the difficulty of evaluating the normalizing constant. In this paper, we first provide a review of methods which yield crude approximations to the MLE. We also review methods based on Markov chain Monte Carlo techniques for which exact MLE has become feasible. We then present a comparative simulation study of the performance of such methods of estimation based on two simulation techniques, the Gibbs sampler and the Metropolis‐Hastings algorithm, carried out for the Strauss model.

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  • Jorge Mateu & Francisco Montes, 2001. "Likelihood Inference for Gibbs Processes in the Analysis of Spatial Point Patterns," International Statistical Review, International Statistical Institute, vol. 69(1), pages 81-104, April.
    • Handle: RePEc:bla:istatr:v:69:y:2001:i:1:p:81-104
    DOI: 10.1111/j.1751-5823.2001.tb00481.x
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    Cited by:

    1. Vinayak Rao & Ryan P. Adams & David D. Dunson, 2017. "Bayesian inference for Matérn repulsive processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 877-897, June.
    2. Matthew Bognar, 2008. "Bayesian modeling of continuously marked spatial point patterns," Computational Statistics, Springer, vol. 23(3), pages 361-379, July.
    3. Jorge Mateu & Francisco Montes, 2001. "Pseudo-likelihood Inference for Gibbs Processes with Exponential Families through Generalized Linear Models," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 125-154, May.
    4. Bognar, Matthew A., 2005. "Bayesian inference for spatially inhomogeneous pairwise interacting point processes," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 1-18, April.

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