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Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range

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  • Rajala, T.
  • Penttinen, A.

Abstract

A Bayesian solution is suggested for the modelling of spatial point patterns with inhomogeneous hard-core radius using Gaussian processes in the regularization. The key observation is that a straightforward use of the finite Gibbs hard-core process likelihood together with a log-Gaussian random field prior does not work without penalisation towards high local packing density. Instead, a nearest neighbour Gibbs process likelihood is used. This approach to hard-core inhomogeneity is an alternative to the transformation inhomogeneous hard-core modelling. The computations are based on recent Markovian approximation results for Gaussian fields. As an application, data on the nest locations of Sand Martin (Riparia riparia) colony11Dataset is attached to the online version. on a vertical sand bank are analysed.

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  • Rajala, T. & Penttinen, A., 2014. "Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 530-541.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:530-541
    DOI: 10.1016/j.csda.2012.08.014
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    References listed on IDEAS

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    1. S. Mase & J. Møller & D. Stoyan & R. Waagepetersen & G. Döge, 2001. "Packing Densities and Simulated Tempering for Hard Core Gibbs Point Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 661-680, December.
    2. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    3. van Lieshout, M.N.M. & Stoica, R.S., 2006. "Perfect simulation for marked point processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 679-698, November.
    4. Linda Stougaard Nielsen & Eva B. Vedel Jensen, 2004. "Statistical Inference for Transformation Inhomogeneous Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 131-142, March.
    5. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    6. J. Møller & A. N. Pettitt & R. Reeves & K. K. Berthelsen, 2006. "An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants," Biometrika, Biometrika Trust, vol. 93(2), pages 451-458, June.
    7. 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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    Cited by:

    1. Ute Hahn & Eva B. Vedel Jensen, 2016. "Hidden Second-order Stationary Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 455-475, June.

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