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

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Illian_2016_Biometrika_GoingOffGrid_AAM.pdf (1.894Mb)
Date
03/2016
Author
Simpson, Daniel
Illian, Janine Baerbel
Lindgren, Finn
Sørbye , Sigrunn H.
Rue, Haavard
Keywords
Approximation of Gaussian random fields
Gaussian Markov random field
Integrated nested Laplace approximation
Spatial point process
Stochastic partial differential equation
GC Oceanography
QA75 Electronic computers. Computer science
3rd-NDAS
BDC
R2C
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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.
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
DOI
https://doi.org/10.1093/biomet/asv064
ISSN
0006-3444
Type
Journal article
Rights
© 2016 Biometrika Trust. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://dx.doi.org/10.1093/biomet/asv064
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  • University of St Andrews Research
URL
http://www.math.ntnu.no/~daniesi/S10-2011.pdf
URI
http://hdl.handle.net/10023/10232

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