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

Kristian Bjørn Hessellund, Ganggang Xu, Yongtao Guan, Rasmus Waagepetersen

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
StateAccepted/In press - 2021


  • case-control
  • composite likelihood
  • conditional likelihood
  • cross pair correlation function
  • multivariate
  • pair correlation function
  • point process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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