Modern environmental and climatological studies produce multiple outcomes at high spatial resolutions. Multivariate spatial modeling is an established means to quantify cross-correlation among outcomes. However, existing models typically suffer from poor computational efficiency and lack the flexibility to simultaneously estimate auto- and cross-covariance structures. In this article, we undertake a novel construction of covariance by utilizing spectral convolution and by imposing an inverted Wishart prior on the cross-correlation structure. The cross-correlation structure with this functional inverted Wishart prior flexibly accommodates not only positive but also weak or negative associations among outcomes while preserving spatial resolution. Furthermore, the proposed model is computationally efficient and produces easily interpretable results, including the individual autocovariances and full cross-correlation matrices, as well as a partial cross-correlation matrix reflecting the outcome correlation after excluding the effects caused by spatial convolution. The model is examined using simulated data sets under different scenarios. It is also applied to the data from the North American Regional Climate Change Assessment Program, examining long-term associations between surface outcomes for air temperature, pressure, humidity, and radiation, on the land area of the North American West Coast. Results and predictive performance are compared with findings from approaches using convolution only or coregionalization.

中文翻译：

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贝叶斯多元空间建模的功能倒置 Wishart 应用到区域气候模型数据

现代环境和气候学研究在高空间分辨率下产生多种结果。多元空间建模是量化结果之间互相关的既定手段。然而，现有模型通常存在计算效率低下的问题，并且缺乏同时估计自协方差和互协方差结构的灵活性。在本文中，我们通过利用谱卷积和在互相关结构上施加倒置的 Wishart 先验来进行协方差的新构造。具有这种功能性倒置 Wishart 先验的互相关结构不仅灵活地适应了结果之间的正关联，而且还适应了结果之间的弱或负关联，同时保留了空间分辨率。此外，所提出的模型计算效率高，并产生易于解释的结果，包括个体自协方差和全互相关矩阵，以及在排除空间卷积引起的影响后反映结果相关性的部分互相关矩阵。该模型使用不同场景下的模拟数据集进行检查。它还应用于北美区域气候变化评估计划的数据，检查北美西海岸陆地区域的气温、压力、湿度和辐射的地表结果之间的长期关联。将结果和预测性能与仅使用卷积或共区域化的方法的结果进行比较。以及在排除空间卷积引起的影响后反映结果相关性的部分互相关矩阵。该模型使用不同场景下的模拟数据集进行检查。它还应用于北美区域气候变化评估计划的数据，检查北美西海岸陆地区域的气温、压力、湿度和辐射的地表结果之间的长期关联。将结果和预测性能与仅使用卷积或共区域化的方法的结果进行比较。以及在排除空间卷积引起的影响后反映结果相关性的部分互相关矩阵。该模型使用不同场景下的模拟数据集进行检查。它还应用于北美区域气候变化评估计划的数据，检查北美西海岸陆地区域的气温、压力、湿度和辐射的地表结果之间的长期关联。将结果和预测性能与仅使用卷积或共区域化的方法的结果进行比较。检查北美西海岸陆地区域的气温、压力、湿度和辐射的地表结果之间的长期关联。将结果和预测性能与仅使用卷积或共区域化的方法的结果进行比较。检查北美西海岸陆地区域的气温、压力、湿度和辐射的地表结果之间的长期关联。将结果和预测性能与仅使用卷积或共区域化的方法的结果进行比较。