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We develop Bayesian predictive stacking for geostatistical models. Ourapproach builds an augmented Bayesian linear regression framework that subsumesthe realizations of the spatial random field and delivers exact analyticallytractable posterior inference conditional upon certain spatial processparameters. We subsequently combine such inference by stacking these individualmodels across the range of values of the hyper-parameters. We devise stackingof means and posterior densities in a manner that is computationally efficientwithout the need of iterative algorithms such as Markov chain Monte Carlo(MCMC) and can exploit the benefits of parallel computations. We offer noveltheoretical insights into the resulting inference within an infill asymptoticparadigm and through empirical results showing that stacked inference iscomparable to full sampling-based Bayesian inference at a significantly lowercomputational cost.

Exact Bayesian Geostatistics Using Predictive Stacking