Bayesian Meta-learning Approach for Feasible Large Spatial Analysis

Geostatistical modeling is afflicted by onerous computational effort when the number of observed locations is very large. While there exists a burgeoning literature today that attempts to tackle the so-called "big-n" problems, spatial inference remains unfeasible for moderate data sets on modest computing architectures. Our current contribution resides in the domain of "meta-" approaches where a massive data set is split into smaller data sets, each data set is analyzed independently and the inference from these individual data are combined to approximate fully model-based Bayesian inference. Our specific contribution is to introduce Bayesian predictive stacking in spatial meta-analysis in the context of univariate spatial data. Furthermore, we aim to make inference and uncertainty quantification feasible without excessively demanding hardware settings. Introducing new methodologies, and exploiting existing techniques, the analysis of a massive data set with observations in millions is illustrated.