Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice

Handle URI:
http://hdl.handle.net/10754/597648
Title:
Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice
Authors:
Park, Jincheol; Liang, Faming
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.
Publisher:
Informa UK Limited
Journal:
Journal of Computational and Graphical Statistics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Apr-2012
DOI:
10.1080/10618600.2012.679228
Type:
Article
ISSN:
1061-8600; 1537-2715
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorPark, Jincheolen
dc.contributor.authorLiang, Famingen
dc.date.accessioned2016-02-25T12:43:41Zen
dc.date.available2016-02-25T12:43:41Zen
dc.date.issued2012-04en
dc.identifier.citationPark 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.en
dc.identifier.issn1061-8600en
dc.identifier.issn1537-2715en
dc.identifier.doi10.1080/10618600.2012.679228en
dc.identifier.urihttp://hdl.handle.net/10754/597648en
dc.description.abstractThe 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.en
dc.description.sponsorshipLiang'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.en
dc.publisherInforma UK Limiteden
dc.subjectGaussian random fielden
dc.subjectKrigingen
dc.subjectMarkov chain Monte Carloen
dc.subjectMarkov random fielden
dc.subjectMatrix inversionen
dc.subjectSpatial dataen
dc.titleBayesian Analysis of Geostatistical Models With an Auxiliary Latticeen
dc.typeArticleen
dc.identifier.journalJournal of Computational and Graphical Statisticsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.