Covariance Approximation for Large Multivariate Spatial Datasets with an Application to Multiple Climate Model Errors
The Annals of Applied Statistics, forthcoming article
Huiyan Sang, Mikyoung Jun, and Jianhua Z Huang
“This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that ac- counts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a non-separable and non-stationary 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.”
- Read the paper [PDF]
