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

作者：Simpson, D.^*; Illian, J. B.^*; Lindgren, F.^*; Sorbye, S. H.^*; Rue, H.^*

来源：Biometrika, 2016, 103(1): 49-70.

DOI：10.1093/biomet/asv064

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

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.

• 出版日期2016-3