A full scale approximation of covariance functions for large spatial data sets

Handle URI:
http://hdl.handle.net/10754/597273
Title:
A full scale approximation of covariance functions for large spatial data sets
Authors:
Sang, Huiyan; Huang, Jianhua Z.
Abstract:
Gaussian process models have been widely used in spatial statistics but face tremendous computational challenges for very large data sets. The model fitting and spatial prediction of such models typically require O(n 3) operations for a data set of size n. Various approximations of the covariance functions have been introduced to reduce the computational cost. However, most existing approximations cannot simultaneously capture both the large- and the small-scale spatial dependence. A new approximation scheme is developed to provide a high quality approximation to the covariance function at both the large and the small spatial scales. The new approximation is the summation of two parts: a reduced rank covariance and a compactly supported covariance obtained by tapering the covariance of the residual of the reduced rank approximation. Whereas the former part mainly captures the large-scale spatial variation, the latter part captures the small-scale, local variation that is unexplained by the former part. By combining the reduced rank representation and sparse matrix techniques, our approach allows for efficient computation for maximum likelihood estimation, spatial prediction and Bayesian inference. We illustrate the new approach with simulated and real data sets. © 2011 Royal Statistical Society.
Citation:
Sang H, Huang JZ (2011) A full scale approximation of covariance functions for large spatial data sets. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 74: 111–132. Available: http://dx.doi.org/10.1111/j.1467-9868.2011.01007.x.
Publisher:
Wiley-Blackwell
Journal:
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
10-Oct-2011
DOI:
10.1111/j.1467-9868.2011.01007.x
Type:
Article
ISSN:
1369-7412
Sponsors:
The research of Huiyan Sang and Jianhua Z. Huang was partially sponsored by NationalScience Foundation grant DMS-1007618. Jianhua Z. Huang’s work was also partially supported by National Science Foundation grant DMS-09-07170 and National Cancer Institute grant CA57030. Both authors were supported by award KUS-CI-016-04, made by KingAbdullah University of Science and Technology. The authors thank the referees and theeditors for valuable comments. The authors also thank Dr Sudipto Banerjee, Dr ReinhardFurrer and Dr Lan Zhou for several useful discussions regarding this work, and they thankDr Cari Kaufman for providing the precipitation data set.
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Full metadata record

DC FieldValue Language
dc.contributor.authorSang, Huiyanen
dc.contributor.authorHuang, Jianhua Z.en
dc.date.accessioned2016-02-25T12:29:33Zen
dc.date.available2016-02-25T12:29:33Zen
dc.date.issued2011-10-10en
dc.identifier.citationSang H, Huang JZ (2011) A full scale approximation of covariance functions for large spatial data sets. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 74: 111–132. Available: http://dx.doi.org/10.1111/j.1467-9868.2011.01007.x.en
dc.identifier.issn1369-7412en
dc.identifier.doi10.1111/j.1467-9868.2011.01007.xen
dc.identifier.urihttp://hdl.handle.net/10754/597273en
dc.description.abstractGaussian process models have been widely used in spatial statistics but face tremendous computational challenges for very large data sets. The model fitting and spatial prediction of such models typically require O(n 3) operations for a data set of size n. Various approximations of the covariance functions have been introduced to reduce the computational cost. However, most existing approximations cannot simultaneously capture both the large- and the small-scale spatial dependence. A new approximation scheme is developed to provide a high quality approximation to the covariance function at both the large and the small spatial scales. The new approximation is the summation of two parts: a reduced rank covariance and a compactly supported covariance obtained by tapering the covariance of the residual of the reduced rank approximation. Whereas the former part mainly captures the large-scale spatial variation, the latter part captures the small-scale, local variation that is unexplained by the former part. By combining the reduced rank representation and sparse matrix techniques, our approach allows for efficient computation for maximum likelihood estimation, spatial prediction and Bayesian inference. We illustrate the new approach with simulated and real data sets. © 2011 Royal Statistical Society.en
dc.description.sponsorshipThe research of Huiyan Sang and Jianhua Z. Huang was partially sponsored by NationalScience Foundation grant DMS-1007618. Jianhua Z. Huang’s work was also partially supported by National Science Foundation grant DMS-09-07170 and National Cancer Institute grant CA57030. Both authors were supported by award KUS-CI-016-04, made by KingAbdullah University of Science and Technology. The authors thank the referees and theeditors for valuable comments. The authors also thank Dr Sudipto Banerjee, Dr ReinhardFurrer and Dr Lan Zhou for several useful discussions regarding this work, and they thankDr Cari Kaufman for providing the precipitation data set.en
dc.publisherWiley-Blackwellen
dc.subjectCovariance functionen
dc.subjectGaussian processesen
dc.subjectGeostatisticsen
dc.subjectKrigingen
dc.subjectLarge spatial data seten
dc.subjectSpatial processesen
dc.titleA full scale approximation of covariance functions for large spatial data setsen
dc.typeArticleen
dc.identifier.journalJournal of the Royal Statistical Society: Series B (Statistical Methodology)en
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-CI-016-04en
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