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

Huiyan Sang, Mikyoung Jun, Jianhua Z. Huang

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)2519-2548
Number of pages30
JournalThe Annals of Applied Statistics
Volume5
Issue number4
DOIs
StatePublished - Dec 2011
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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