Exact Bayesian Geostatistics Using Predictive Stacking

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.