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Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes

Author

Listed:
  • Kristian Bjørn Hessellund
  • Ganggang Xu
  • Yongtao Guan
  • Rasmus Waagepetersen

Abstract

This paper introduces a new approach to inferring the second‐order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi‐parametric model for the multivariate intensity function containing an unspecified complex factor common to all types of points. Given this model, we construct a second‐order conditional composite likelihood to infer the pair correlation and cross pair correlation functions of the LGCP. Crucially this likelihood does not depend on the unspecified part of the intensity function. We also introduce a cross‐validation method for model selection and an algorithm for regularized inference that can be used to obtain sparse models for cross pair correlation functions. The methodology is applied to simulated data as well as data examples from microscopy and criminology. This shows how the new approach outperforms existing alternatives where the intensity functions are estimated non‐parametrically.

Suggested Citation

  • Kristian Bjørn Hessellund & Ganggang Xu & Yongtao Guan & Rasmus Waagepetersen, 2022. "Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 244-268, January.
    • Handle: RePEc:bla:jorssc:v:71:y:2022:i:1:p:244-268
    DOI: 10.1111/rssc.12530
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    References listed on IDEAS

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