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Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection

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  • T. Rajala
  • D. J. Murrell
  • S. C. Olhede

Abstract

We propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology thus develops high dimensional data understanding in the point process setting. The method is based on modelling the patterns by using a flexible Gibbs point process model to characterize point‐to‐point interactions at different spatial scales directly. By using the Gibbs framework significant interactions can also be captured at small scales. Subsequently, the Gibbs point process is fitted by using a pseudolikelihood approximation, and we select significant interactions automatically by using the group lasso penalty with this likelihood approximation. Thus we estimate the multivariate interactions stably even in this setting. We demonstrate the feasibility of the method with a simulation study and show its power by applying it to a large and complex rainforest plant population data set of 83 species.

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  • 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.
    • Handle: RePEc:bla:jorssc:v:67:y:2018:i:5:p:1237-1273
    DOI: 10.1111/rssc.12281
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    1. Kristian Bjørn Hessellund & Ganggang Xu & Yongtao Guan & Rasmus Waagepetersen, 2022. "Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 244-268, January.
    2. James S. Martin & David J. Murrell & Sofia C. Olhede, 2023. "Multivariate geometric anisotropic Cox processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1420-1465, September.
    3. Ismaïla Ba & Jean‐François Coeurjolly, 2023. "Inference for low‐ and high‐dimensional inhomogeneous Gibbs point processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 993-1021, September.
    4. Eckardt, Matthias & González, Jonatan A. & Mateu, Jorge, 2021. "Graphical modelling and partial characteristics for multitype and multivariate-marked spatio-temporal point processes," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    5. Ian Flint & Nick Golding & Peter Vesk & Yan Wang & Aihua Xia, 2022. "The saturated pairwise interaction Gibbs point process as a joint species distribution model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1721-1752, November.

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