期刊
BIOMETRIKA
卷 103, 期 1, 页码 49-70出版社
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asv064
关键词
Approximation of Gaussian random fields; Gaussian Markov random field; Integrated nested Laplace approximation; Spatial point process; Stochastic partial differential equation
资金
- Research Councils UK
- U.S. National Science Foundation
- Center for Tropical Forest Science
- Smithsonian Tropical Research Institute
- John D. and Catherine T. MacArthur Foundation
- Mellon Foundation
- Small World Institute Fund
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.
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