Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms for posterior sampling of the latent process, but these may exhibit pathological behavior in estimating covariance parameters. In this article, we introduce gridding and parameter expansion methods to improve the practical performance of MCMC algorithms in terms of effective sample size per unit time (ESS/s). Gridding is a model-based strategy that reduces the number of expensive operations necessary during MCMC on irregularly spaced data. Parameter expansion reduces dependence in posterior samples in spatial regression for high resolution data. These two strategies lead to computational gains in the big data settings on which we focus. We consider popular constructions of univariate spatial processes based on Mat\'ern covariance functions and multivariate coregionalization models for Gaussian outcomes in extensive analyses of synthetic datasets comparing with alternative methods. We demonstrate effectiveness of our proposed methods in a forestry application using remotely sensed data from NASA's Goddard LiDAR, Hyper-Spectral, and Thermal imager (G-LiHT).

翻译：针对海量数据集的可扩展空间高斯过程可通过稀疏有向无环图构建，其中少量有向边足以灵活刻画空间依赖性。该有向无环图可用于设计潜过程后验采样的快速算法，但这些算法在估计协方差参数时可能出现病态行为。本文引入网格化与参数扩展方法，以提升MCMC算法在单位时间有效样本量方面的实际性能。网格化是一种基于模型的策略，可减少不规则分布数据在MCMC过程中所需的高成本运算次数。参数扩展则能降低高分辨率数据空间回归中后验样本的依赖性。这两种策略在我们关注的大数据场景中实现了计算效率的提升。通过合成数据集的广泛分析，我们基于Matérn协方差函数构建了流行的单变量空间过程模型，并针对高斯结果建立了多元协同区域化模型，同时与替代方法进行比较。利用美国宇航局戈达德激光雷达、高光谱与热成像仪获取的遥感数据，我们在林业应用中验证了所提方法的有效性。