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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. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    2. Jean-François Coeurjolly & Ege Rubak, 2013. "Fast Covariance Estimation for Innovations Computed from a Spatial Gibbs Point Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 669-684, December.
    3. Radu S. Stoica & Vicent J. Martínez & Enn Saar, 2007. "A three‐dimensional object point process for detection of cosmic filaments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 459-477, August.
    4. Jean-François Coeurjolly & Frédéric Lavancier, 2013. "Residuals and goodness-of-fit tests for stationary marked Gibbs point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 247-276, March.
    5. Frédéric Lavancier & Jesper Møller, 2016. "Modelling Aggregation on the Large Scale and Regularity on the Small Scale in Spatial Point Pattern Datasets," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 587-609, June.
    6. Alan Gelfand & Alexandra Schmidt & Sudipto Banerjee & C. Sirmans, 2004. "Nonstationary multivariate process modeling through spatially varying coregionalization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 263-312, December.
    7. Mohler, G. O. & Short, M. B. & Brantingham, P. J. & Schoenberg, F. P. & Tita, G. E., 2011. "Self-Exciting Point Process Modeling of Crime," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 100-108.
    8. Grabarnik, Pavel & Särkkä, Aila, 2009. "Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions," Ecological Modelling, Elsevier, vol. 220(9), pages 1232-1240.
    9. Scheipl, Fabian, 2011. "spikeSlabGAM: Bayesian Variable Selection, Model Choice and Regularization for Generalized Additive Mixed Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i14).
    10. Adrian Baddeley & Jean-François Coeurjolly & Ege Rubak & Rasmus Waagepetersen, 2014. "Logistic regression for spatial Gibbs point processes," Biometrika, Biometrika Trust, vol. 101(2), pages 377-392.
    11. Anders Brix & Jesper Moller, 2001. "Space‐time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 471-488, September.
    12. Peter Diggle & Pingping Zheng & Peter Durr, 2005. "Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 645-658, June.
    13. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    14. Rasmus Waagepetersen & Yongtao Guan & Abdollah Jalilian & Jorge Mateu, 2016. "Analysis of multispecies point patterns by using multivariate log-Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(1), pages 77-96, January.
    15. A. Baddeley & M. Lieshout, 1995. "Area-interaction point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 601-619, December.
    16. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    17. 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).
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    2. 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.
    3. 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.

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