Open Access
December 2011 Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors
Huiyan Sang, Mikyoung Jun, Jianhua Z. Huang
Ann. Appl. Stat. 5(4): 2519-2548 (December 2011). DOI: 10.1214/11-AOAS478


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.


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Huiyan Sang. Mikyoung Jun. Jianhua Z. Huang. "Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors." Ann. Appl. Stat. 5 (4) 2519 - 2548, December 2011.


Published: December 2011
First available in Project Euclid: 20 December 2011

zbMATH: 1234.62071
MathSciNet: MR2907125
Digital Object Identifier: 10.1214/11-AOAS478

Keywords: Climate model output , co-regionalization , Gaussian processes , large spatial data set , multivariate spatial process

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.5 • No. 4 • December 2011
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