The Annals of Applied Statistics

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

Huiyan Sang, Mikyoung Jun, and Jianhua Z. Huang

Full-text: Open access

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.

Article information

Source
Ann. Appl. Stat., Volume 5, Number 4 (2011), 2519-2548.

Dates
First available in Project Euclid: 20 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1324399605

Digital Object Identifier
doi:10.1214/11-AOAS478

Mathematical Reviews number (MathSciNet)
MR2907125

Zentralblatt MATH identifier
1234.62071

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

Citation

Sang, Huiyan; Jun, Mikyoung; Huang, Jianhua Z. Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors. Ann. Appl. Stat. 5 (2011), no. 4, 2519--2548. doi:10.1214/11-AOAS478. https://projecteuclid.org/euclid.aoas/1324399605


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