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

D. Simpson, Janine B. Illian, F. Lindgren, S. H. Sorbye, H. Rue

Research output: Contribution to journalArticle

42 Citations (Scopus)
23 Downloads (Pure)

Abstract

This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel 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, while an approximation based on a counting process on a partition of the domain only achieves first-order convergence. The given results improve on the general theory of convergence of the stochastic partial differential equation models, introduced by Lindgren et al. (2011). The new method is demonstrated on a standard point pattern data set 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
Early online date5 Feb 2016
DOIs
Publication statusPublished - 1 Mar 2016

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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    Simpson, D., Illian, J. B., Lindgren, F., Sorbye, S. H., & Rue, H. (2016). Going off grid: computationally efficient inference for log-Gaussian Cox processes. Biometrika, 103(1), 49-70. https://doi.org/10.1093/biomet/asv064