With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial data sets. This has generated substantial interest over the last decade, already too vast to be summarized here, in scalable methodologies for analyzing large spatial data sets. Scalable spatial process models have been found especially attractive due to their richness and flexibility and, particularly so in the Bayesian paradigm, due to their presence in hierarchical model settings. However, the vast majority of research articles present in this domain have been geared toward innovative theory or more complex model development. Very limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article devises massively scalable Bayesian approaches that can rapidly deliver inference on spatial process that are practically indistinguishable from inference obtained using more expensive alternatives. A key emphasis is on implementation within very standard (modest) computing environments (eg, a standard desktop or laptop) using easily available statistical software packages. Key insights are offered regarding assumptions and approximations concerning practical efficiency.

中文翻译：

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在适度计算环境下对海量空间数据集进行实用贝叶斯建模和推理†

随着地理信息系统和相关计算技术的不断进步，统计学家经常需要分析非常大的空间数据集。在过去的十年里，这引起了人们对分析大型空间数据集的可扩展方法的极大兴趣，已经太大而无法在此概括。可扩展的空间过程模型因其丰富性和灵活性而特别有吸引力，尤其是在贝叶斯范式中，因为它们存在于分层模型设置中。然而，该领域的绝大多数研究文章都是针对创新理论或更复杂的模型开发。对于实践科学家或空间分析师易于实现的可扩展分层模型的方法，人们的关注非常有限。本文设计了大规模可扩展的贝叶斯方法，可以快速提供空间过程的推理，这与使用更昂贵的替代方案获得的推理几乎没有区别。重点是使用易于获得的统计软件包在非常标准（适度）的计算环境（例如标准台式机或笔记本电脑）中实现。提供了有关实际效率的假设和近似值的关键见解。