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We propose a method for detecting significant interactions in very largemultivariate spatial point patterns. This methodology develops high dimensionaldata understanding in the point process setting. The method is based onmodelling the patterns using a flexible Gibbs point process model to directlycharacterise point-to-point interactions at different spatial scales. By usingthe Gibbs framework significant interactions can also be captured at smallscales. Subsequently, the Gibbs point process is fitted using apseudo-likelihood approximation, and we select significant interactionsautomatically using the group lasso penalty with this likelihood approximation.Thus we estimate the multivariate interactions stably even in this setting. Wedemonstrate the feasibility of the method with a simulation study and show itspower by applying it to a large and complex rainforest plant population dataset of 83 species.

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