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

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Author(s)

Daniel Simpson, Janine Baerbel Illian, Finn Lindgren, Sigrunn H. Sørbye , Haavard Rue

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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.
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Original languageEnglish
Pages (from-to)49-70
JournalBiometrika
Volume103
Issue number1
Early online date5 Feb 2016
DOIs
StatePublished - Mar 2016

    Research areas

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

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