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 |
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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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