Going off grid : computationally efficient inference for log-Gaussian Cox processes
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.
Citation
Simpson , D , Illian , J B , Lindgren , F , Sørbye , S H & Rue , H 2016 , ' Going off grid : computationally efficient inference for log-Gaussian Cox processes ' , Biometrika , vol. 103 , no. 1 , pp. 49-70 . https://doi.org/10.1093/biomet/asv064
Publication
Biometrika
Status
Peer reviewed
ISSN
0006-3444Type
Journal article
Collections
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