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

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

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

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Illian, Professor Janine
Authors: Simpson, D., Illian, J.B., Lindgren, F., Sørbye, S.H., and Rue, H.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Biometrika
Publisher:Oxford University Press
ISSN:0006-3444
ISSN (Online):1464-3510
Published Online:05 February 2016

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