We develop Bayesian predictive stacking for geostatistical models. Our approach builds an augmented Bayesian linear regression framework that subsumes the realizations of the spatial random field and delivers exact analytically tractable posterior inference conditional upon certain spatial process parameters. We subsequently combine such inference by stacking these individual models across the range of values of the hyper-parameters. We devise stacking of means and posterior densities in a manner that is computationally efficient without the need of iterative algorithms such as Markov chain Monte Carlo (MCMC) and can exploit the benefits of parallel computations. We offer novel theoretical insights into the resulting inference within an infill asymptotic paradigm and through empirical results showing that stacked inference is comparable to full sampling-based Bayesian inference at a significantly lower computational cost.

翻译：我们针对地质统计模型开发了贝叶斯预测堆叠方法。该方法构建了一个增广贝叶斯线性回归框架，将空间随机场的实现纳入其中，并在给定某些空间过程参数条件下推导出精确的可解析后验推断。随后，我们通过跨超参数取值范围堆叠这些独立模型来整合此类推断。我们设计了均值与后验密度的堆叠方式，该方法无需马尔可夫链蒙特卡洛（MCMC）等迭代算法即可实现高效计算，并能充分利用并行计算优势。通过渐进填充渐近范式下的理论分析及实证结果表明，在显著降低计算成本的前提下，堆叠推断可达到与基于全采样贝叶斯推断相当的性能。