Joint modeling of spatially oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes and the spatial dependence for each outcome. Such modeling is now sought for massive data sets with variables measured at a very large number of locations. Bayesian inference, while attractive for accommodating uncertainties through hierarchical structures, can become computationally onerous for modeling massive spatial data sets because of its reliance on iterative estimation algorithms. This article develops a conjugate Bayesian framework for analyzing multivariate spatial data using analytically tractable posterior distributions that obviate iterative algorithms. We discuss differences between modeling the multivariate response itself as a spatial process and that of modeling a latent process in a hierarchical model. We illustrate the computational and inferential benefits of these models using simulation studies and analysis of a vegetation index data set with spatially dependent observations numbering in the millions.

中文翻译：

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高维多元地统计学：贝叶斯矩阵正态方法

在环境科学中，面向空间的因变量的联合建模在环境科学中是司空见惯的，科学家试图估算一组环境结果之间的关系，以说明这些结果之间的依赖性以及每个结果的空间依赖性。现在正在寻求这样的建模，以用于具有在非常多个位置处测量的变量的海量数据集。贝叶斯推理虽然通过层次结构来适应不确定性很有吸引力，但由于它依赖于迭代估计算法，因此在建模大型空间数据集方面可能会在计算上变得繁重。本文开发了一种共轭贝叶斯框架，该框架使用避免迭代算法的易分析的后验分布来分析多元空间数据。我们讨论了将多元响应本身建模为空间过程与将潜在过程建模为层次模型之间的区别。我们使用仿真研究和对植被指数数据集的分析来说明这些模型的计算和推断优势，其中植被指数数据集具有数以百万计的空间相关观测值。