Enhancing Bayesian Distributed Learning with Spatially Adjusted Predictive Distributions

Many novel methodologies for solving large spatial problems leverage distributed learning settings. Most follow the Divide-and-Conquer paradigm, which analyzes independently local subregions and then aggregates posterior inferences. These approaches often rely on any convex combination of local posterior distributions, i.e., convex mixtures of posterior distributions regulated by normalized weights. This manuscript proposes an effective method for mitigating partition dependence by adjusting the normalized weights, extending the applicability of such methods beyond randomly assigned partitions. While the Divide-and-Conquer approach is computationally efficient and often highly effective, its dependence on the spatial characteristics of the data partition can seriously impact inference, as emerged in several previous studies. Addressing performance issues in regular-grid spatial partitions, where distributed learning models often struggle, may be impactful. This contribution could support the latest developments in distributed learning for spatial problems, overcoming previous limitations. A climate science application on global warming data demonstrates effectiveness in interpolating sea surface temperature worldwide.