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Hybrids of Gibbs Point Process Models and Their Implementation

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  • Baddeley, Adrian
  • Turner, Rolf
  • Mateu, Jorge
  • Bevan, Andrew

Abstract

We describe a simple way to construct new statistical models for spatial point pattern data. Taking two or more existing models (finite Gibbs spatial point processes) we multiply the probability densities together and renormalise to obtain a new probability density. We call the resulting model a hybrid. We discuss stochastic properties of hybrids, their statistical implications, statistical inference, computational strategies and software implementation in the R package spatstat. Hybrids are particularly useful for constructing models which exhibit interaction at different spatial scales. The methods are demonstrated on a real data set on human social interaction. Software and data are provided.

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  • Baddeley, Adrian & Turner, Rolf & Mateu, Jorge & Bevan, Andrew, 2013. "Hybrids of Gibbs Point Process Models and Their Implementation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i11).
    • Handle: RePEc:jss:jstsof:v:055:i11
    DOI: http://hdl.handle.net/10.18637/jss.v055.i11
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    References listed on IDEAS

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    1. Jens Jensen & Hans Künsch, 1994. "On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(3), pages 475-486, September.
    2. Nicolas Picard & Avner Bar‐Hen & Frédéric Mortier & Joël Chadœuf, 2009. "The Multi‐scale Marked Area‐interaction Point Process: A Model for the Spatial Pattern of Trees," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 23-41, March.
    3. Bo-Cheng Wei & Jian-Qing Shi & Wing-Kam Fung & Yue-Qing Hu, 1998. "Testing for Varying Dispersion in Exponential Family Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 277-294, June.
    4. Kasper K. Berthelsen & Jesper Møller, 2003. "Likelihood and Non‐parametric Bayesian MCMC Inference for Spatial Point Processes Based on Perfect Simulation and Path Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 549-564, September.
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    2. Yolanda Caballero & Ramón Giraldo & Jorge Mateu, 2022. "A spatial randomness test based on the box-counting dimension," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(3), pages 499-524, September.
    3. T. Rajala & D. J. Murrell & S. C. Olhede, 2018. "Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1237-1273, November.
    4. Daniel, Jeffrey & Horrocks, Julie & Umphrey, Gary J., 2018. "Penalized composite likelihoods for inhomogeneous Gibbs point process models," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 104-116.
    5. Ninna Vihrs & Jesper Møller & Alan E. Gelfand, 2022. "Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 185-210, March.
    6. José Ramón Martínez Batlle & Yntze van der Hoek, 2018. "Clusters of high abundance of plants detected from local indicators of spatial association (LISA) in a semi-deciduous tropical forest," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-16, December.

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