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Multivariate geometric anisotropic Cox processes

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  • James S. Martin
  • David J. Murrell
  • Sofia C. Olhede

Abstract

This paper introduces a new modeling and inference framework for multivariate and anisotropic point processes. Building on recent innovations in multivariate spatial statistics, we propose a new family of multivariate anisotropic random fields, and from them a family of anisotropic point processes. We give conditions that make the proposed models valid. We also propose a Palm likelihood‐based inference method for this type of point process, circumventing issues of likelihood tractability. Finally we illustrate the utility of the proposed modeling framework by analyzing spatial ecological observations of plants and trees in the Barro Colorado Island data.

Suggested Citation

  • James S. Martin & David J. Murrell & Sofia C. Olhede, 2023. "Multivariate geometric anisotropic Cox processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1420-1465, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1420-1465
    DOI: 10.1111/sjos.12640
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