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

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 t...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society Series C: Applied Statistics 2018-11, Vol.67 (5), p.1237-1273
Main Authors: Rajala, T., Murrell, D. J., Olhede, S. C.
Format: Article
Language:English
Subjects:
Approximation
Barro Colorado Island
Computer simulation
Feasibility
Feasibility studies
Gibbs models
Mathematical analysis
Multivariate point patterns
Power
Rainforests
Simulation
Species interaction
Variable selection
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Summary: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.
ISSN:0035-9254
1467-9876
DOI:10.1111/rssc.12281