This work extends earlier work on spatial meta kriging for the analysis of large multivariate spatial datasets as commonly encountered in environmental and climate sciences. Spatial meta-kriging partitions the data into subsets, analyzes each subset using a Bayesian spatial process model and then obtains approximate posterior inference for the entire dataset by optimally combining the individual posterior distributions from each subset. Importantly, as is often desired in spatial analysis, spatial meta kriging offers posterior predictive inference at arbitrary locations for the outcome as well as the residual spatial surface after accounting for spatially oriented predictors. Our current work explores spatial meta kriging idea to enhance scalability of multivariate spatial Gaussian process model that uses linear model co-regionalization (LMC) to account for the correlation between multiple components. The approach is simple, intuitive and scales multivariate spatial process models to big data effortlessly. A simulation study reveals inferential and predictive accuracy offered by spatial meta kriging on multivariate observations.

中文翻译：

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多元空间元克里金法

这项工作扩展了空间元克里金法的早期工作，用于分析环境和气候科学中常见的大型多元空间数据集。空间元克里金法将数据划分为子集，使用贝叶斯空间过程模型分析每个子集，然后通过优化组合每个子集的各个后验分布来获得整个数据集的近似后验推断。重要的是，正如空间分析中经常需要的那样，空间元克里金法在任意位置提供结果的后验预测推理，以及考虑空间定向预测变量后的剩余空间表面。我们当前的工作探索空间元克里金法思想，以增强多元空间高斯过程模型的可扩展性，该模型使用线性模型共区域化（LMC）来解释多个分量之间的相关性。该方法简单、直观，可以轻松地将多元空间过程模型扩展到大数据。模拟研究揭示了空间元克里金法对多变量观测提供的推理和预测准确性。