Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors

Handle URI:
http://hdl.handle.net/10754/597892
Title:
Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors
Authors:
Sang, Huiyan; Jun, Mikyoung; Huang, Jianhua Z.
Abstract:
This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial dependence, and a sparse covariance matrix to correct the small-scale dependence error induced by the reduced rank approximation. We pay special attention to the case that the second part of the approximation has a block-diagonal structure. Simulation results of model fitting and prediction show substantial improvement of the proposed approximation over the predictive process approximation and the independent blocks analysis. We then apply our computational approach to the joint statistical modeling of multiple climate model errors. © 2012 Institute of Mathematical Statistics.
Citation:
Sang H, Jun M, Huang JZ (2011) Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors. The Annals of Applied Statistics 5: 2519–2548. Available: http://dx.doi.org/10.1214/11-AOAS478.
Publisher:
Institute of Mathematical Statistics
Journal:
The Annals of Applied Statistics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Dec-2011
DOI:
10.1214/11-AOAS478
Type:
Article
ISSN:
1932-6157
Sponsors:
This publication is based in part on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).Supported in part by NSF Grant DMS-10-07618.Supported in part by NSF Grant DMS-09-06532.Supported in part by NSF Grant DMS-09-07170 and the NCI Grant CA57030.
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Full metadata record

DC FieldValue Language
dc.contributor.authorSang, Huiyanen
dc.contributor.authorJun, Mikyoungen
dc.contributor.authorHuang, Jianhua Z.en
dc.date.accessioned2016-02-25T12:58:27Zen
dc.date.available2016-02-25T12:58:27Zen
dc.date.issued2011-12en
dc.identifier.citationSang H, Jun M, Huang JZ (2011) Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors. The Annals of Applied Statistics 5: 2519–2548. Available: http://dx.doi.org/10.1214/11-AOAS478.en
dc.identifier.issn1932-6157en
dc.identifier.doi10.1214/11-AOAS478en
dc.identifier.urihttp://hdl.handle.net/10754/597892en
dc.description.abstractThis paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial dependence, and a sparse covariance matrix to correct the small-scale dependence error induced by the reduced rank approximation. We pay special attention to the case that the second part of the approximation has a block-diagonal structure. Simulation results of model fitting and prediction show substantial improvement of the proposed approximation over the predictive process approximation and the independent blocks analysis. We then apply our computational approach to the joint statistical modeling of multiple climate model errors. © 2012 Institute of Mathematical Statistics.en
dc.description.sponsorshipThis publication is based in part on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).Supported in part by NSF Grant DMS-10-07618.Supported in part by NSF Grant DMS-09-06532.Supported in part by NSF Grant DMS-09-07170 and the NCI Grant CA57030.en
dc.publisherInstitute of Mathematical Statisticsen
dc.subjectClimate model outputen
dc.subjectCo-regionalizationen
dc.subjectGaussian processesen
dc.subjectLarge spatial data seten
dc.subjectMultivariate spatial processen
dc.titleCovariance approximation for large multivariate spatial data sets with an application to multiple climate model errorsen
dc.typeArticleen
dc.identifier.journalThe Annals of Applied Statisticsen
kaust.grant.numberKUS-C1-016-04en
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