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    Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice

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    Type
    Article
    Authors
    Park, Jincheol
    Liang, Faming
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2012-06-14
    Online Publication Date
    2012-06-14
    Print Publication Date
    2012-04
    Permanent link to this record
    http://hdl.handle.net/10754/597648
    
    Metadata
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    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.
    Sponsors
    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
    ae974a485f413a2113503eed53cd6c53
    10.1080/10618600.2012.679228
    Scopus Count
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