Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice

Type
Article

Authors
Park, Jincheol
Liang, Faming

KAUST Grant Number
KUS-C1-016-04

Online Publication Date
2012-06-14

Print Publication Date
2012-04

Date
2012-06-14

Abstract
The Gaussian geostatistical model has been widely used for modeling spatial data. However, this model suffers from a severe difficulty in computation: it requires users to invert a large covariance matrix. This is infeasible when the number of observations is large. In this article, we propose an auxiliary lattice-based approach for tackling this difficulty. By introducing an auxiliary lattice to the space of observations and defining a Gaussian Markov random field on the auxiliary lattice, our model completely avoids the requirement of matrix inversion. It is remarkable that the computational complexity of our method is only O(n), where n is the number of observations. Hence, our method can be applied to very large datasets with reasonable computational (CPU) times. The numerical results indicate that our model can approximate Gaussian random fields very well in terms of predictions, even for those with long correlation lengths. For real data examples, our model can generally outperform conventional Gaussian random field models in both prediction errors and CPU times. Supplemental materials for the article are available online. © 2012 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Citation
Park J, Liang F (2012) Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice. Journal of Computational and Graphical Statistics 21: 453–475. Available: http://dx.doi.org/10.1080/10618600.2012.679228.

Acknowledgements
Liang's research was partially supported by grants from the National Science Foundation (DMS-1007457 and CMMI-0926803) and the award (KUS-C1-016-04) made by King Abdullah University of Science and Technology (KAUST). We thank the Editor, Associate editor, and three referees for their constructive comments, which have led to significant improvement of this article.

Publisher
Informa UK Limited

Journal
Journal of Computational and Graphical Statistics

DOI
10.1080/10618600.2012.679228

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