Going off grid: computationally efficient inference for log-Gaussian Cox processes

D. Simpson, J. B. Illian, F. Lindgren, S. H. Sørbye, H. Rue

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57 Citations (Scopus)

Abstract

This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making use of a continuously specified Gaussian random field. We show that for sufficiently smooth Gaussian random field prior distributions, the approximation can converge with arbitrarily high order, whereas an approximation based on a counting process on a partition of the domain achieves only first-order convergence. The results improve upon the general theory of convergence for stochastic partial differential equation models introduced by Lindgren et al. (2011). The new method is demonstrated on a standard point pattern dataset, and two interesting extensions to the classical log-Gaussian Cox process framework are discussed. The first extension considers variable sampling effort throughout the observation window and implements the method of Chakraborty et al. (2011). The second extension constructs a log-Gaussian Cox process on the world's oceans. The analysis is performed using integrated nested Laplace approximation for fast approximate inference.

Original languageEnglish
Pages (from-to)49-70
Number of pages22
JournalBiometrika
Volume103
Issue number1
DOIs
Publication statusPublished - Mar 2016
Externally publishedYes

Keywords

  • Approximation of Gaussian random fields
  • Gaussian Markov random field
  • Integrated nested Laplace approximation
  • Spatial point process
  • Stochastic partial differential equation

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