We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit analytically tractable posterior distributions for regression coefficients of predictors and the realizations of the spatial process conditional upon process parameters. We subsequently combine such inference by stacking these 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 resorting to 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：本文针对地质统计模型开发了贝叶斯预测堆叠方法，其主要推断目标是对潜在空间随机场进行推断，并实现任意位置的空间预测。我们利用回归系数及空间过程在给定过程参数条件下的解析后验分布，通过将不同超参数取值下的模型进行堆叠来整合这些推断结果。我们提出的均值与后验密度堆叠方法无需依赖马尔可夫链蒙特卡洛（MCMC）等迭代算法，具有计算高效性，并可充分利用并行计算的优势。通过填充渐近框架下的理论分析以及实证结果表明，堆叠推断在显著降低计算成本的同时，其推断效果可与全采样贝叶斯方法相媲美。