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Analysing Multivariate Spatial Point Processes with Continuous Marks: A Graphical Modelling Approach

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  • Matthias Eckardt
  • Jorge Mateu

Abstract

This paper discusses the application of graphical modelling in the statistical analysis of marked point patterns. We consider a multivariate planar point process with quantitative marks. After a survey of statistical methods for marked point processes, a new graphical model is presented. The sub‐processes of marked points with identical discrete marks are identified with nodes of a graph, which is used to describe aspects of the spatial relationship: If two sub‐patterns are similar, then an arc is made between the corresponding nodes. Similarity is defined based on spectral densities, which makes the computations efficient. The resulting graph presents all these pairwise similarities simultaneously. We demonstrate the application of our method in the analysis of a multi‐species forest, where the points are tree locations, the discrete marks tree species and the quantitative marks are the diameters at breast height.

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  • Matthias Eckardt & Jorge Mateu, 2019. "Analysing Multivariate Spatial Point Processes with Continuous Marks: A Graphical Modelling Approach," International Statistical Review, International Statistical Institute, vol. 87(1), pages 44-67, April.
    • Handle: RePEc:bla:istatr:v:87:y:2019:i:1:p:44-67
    DOI: 10.1111/insr.12272
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    Cited by:

    1. 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).

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