Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors
Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors
复制标题
大型多元空间数据集的协方差近似及其对多个气候模型误差的应用
DOI：
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发表时间：
2011
期刊：
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通讯作者：
Jianhua Z. Huang
中科院分区：
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作者：
H. Sang;M. Jun;Jianhua Z. Huang
本文研究了多个气候模型误差之间的互相关性。我们建立了一个贝叶斯分层模型，该模型考虑了各个模型的空间依赖性以及不同气候模型之间的交叉协方差。我们的方法允许不可分离且非平稳的互协方差结构。我们还提出了一种协方差近似方法，以促进非常大的多元空间数据集的建模和分析中的计算。协方差近似由两部分组成：用于捕获大规模空间依赖性的降阶部分，以及用于校正由降阶近似引起的小规模依赖性误差的稀疏协方差矩阵。我们特别注意近似的第二部分具有块对角线结构的情况。模型拟合和预测的仿真结果表明，所提出的近似相对于预测过程近似和独立块分析有显着改进。然后，我们将计算方法应用于多个气候模型误差的联合统计建模。
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.