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

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

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.

Suggested Citation

  • D. Simpson & J. B. Illian & F. Lindgren & S. H. Sørbye & H. Rue, 2016. "Going off grid: computationally efficient inference for log-Gaussian Cox processes," Biometrika, Biometrika Trust, vol. 103(1), pages 49-70.
  • Handle: RePEc:oup:biomet:v:103:y:2016:i:1:p:49-70.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv064
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    References listed on IDEAS

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    1. Avishek Chakraborty & Alan E. Gelfand & Adam M. Wilson & Andrew M. Latimer & John A. Silander, 2011. "Point pattern modelling for degraded presence‐only data over large regions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(5), pages 757-776, November.
    2. Peter J. Diggle & Raquel Menezes & Ting‐li Su, 2010. "Geostatistical inference under preferential sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 191-232, March.
    3. Waagepetersen, Rasmus, 2004. "Convergence of posteriors for discretized log Gaussian Cox processes," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 229-235, February.
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    Cited by:

    1. David L. Miller & Richard Glennie & Andrew E. Seaton, 2020. "Understanding the Stochastic Partial Differential Equation Approach to Smoothing," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 1-16, March.
    2. Janine B. Illian & David F. R. P. Burslem, 2017. "Improving the usability of spatial point process methodology: an interdisciplinary dialogue between statistics and ecology," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 495-520, October.
    3. Unn Dahlén & Johan Lindström & Marko Scholze, 2020. "Spatiotemporal reconstructions of global CO2‐fluxes using Gaussian Markov random fields," Environmetrics, John Wiley & Sons, Ltd., vol. 31(4), June.

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