Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models have been proposed that can be easily embedded within a hierarchical modeling framework to carry out Bayesian inference. While the focus of statistical research has mostly been directed toward innovative and more complex model development, relatively limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article discusses how point-referenced spatial process models can be cast as a conjugate Bayesian linear regression that can rapidly deliver inference on spatial processes. The approach allows exact sampling directly (avoids iterative algorithms such as Markov chain Monte Carlo) from the joint posterior distribution of regression parameters, the latent process and the predictive random variables, and can be easily implemented on statistical programming environments such as R.
翻译:统计人员对分析大型空间数据集的可扩缩方法产生了很大兴趣,提出了各种可扩缩的空间过程模型,这些模型可以很容易地嵌入一个等级建模框架,以进行贝叶斯推理;虽然统计研究的重点大多放在创新和更复杂的模型开发上,但对为实际科学家或空间分析员制定易于执行的可扩缩的等级模型的方法的关注相对有限;这篇文章讨论了如何将点参照的空间过程模型作为可迅速提供空间过程推断的贝叶斯线性回归法来进行。这种方法可以直接从回归参数、潜在过程和预测随机变量的近视分布物、回归参数、潜在过程和预测随机变量的预测性等统计性编程环境中进行精确的抽样(避免了马尔科夫链蒙特卡洛等迭代算法),而且很容易在R等统计方案编制环境中实施。