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

## TL;DR

This paper introduces a novel method combining Gibbs point process models and group lasso for detecting significant multivariate spatial interactions at multiple scales in large point pattern datasets, demonstrated on rainforest data.

## Contribution

It develops a high-dimensional approach for identifying multiscale interactions in large spatial point patterns using Gibbs models and automatic variable selection.

## Key findings

- Method effectively detects interactions at various scales.
- Demonstrated on complex rainforest data with 83 species.
- Shows high power and stability in identifying significant interactions.

## Abstract

We propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology develops high dimensional data understanding in the point process setting. The method is based on modelling the patterns using a flexible Gibbs point process model to directly characterise point-to-point interactions at different spatial scales. By using the Gibbs framework significant interactions can also be captured at small scales. Subsequently, the Gibbs point process is fitted using a pseudo-likelihood approximation, and we select significant interactions automatically 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.