🤖 AI Summary
To address computational bottlenecks in latent spatial field inference and pointwise prediction in geostatistical models, this paper proposes Bayesian Predictive Stacking (BPS). BPS analytically aggregates posterior distributions of regression coefficients and spatial processes across multiple hyperparameter configurations, circumventing iterative algorithms such as MCMC and enabling fully parallelized inference. Its key innovation lies in a unified stacking framework that jointly combines predictive means and posterior densities, underpinned by infill asymptotic theory that guarantees statistical consistency. Experiments demonstrate that BPS achieves predictive accuracy comparable to full-sample Bayesian inference while drastically reducing computational time. The method is thus highly efficient, robust to hyperparameter specification, and scalable to large spatial datasets.
📝 Abstract
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.
