Meta-Kriging: Scalable Bayesian Modeling and Inference for Massive Spatial Datasets.

Area of Science:

• Geostatistics
• Bayesian statistics
• Computational statistics

Background:

• Analyzing large spatial datasets with traditional models is computationally intensive.
• Existing methods struggle with scalability for massive geostatistical data.

Purpose of the Study:

• To develop a scalable Bayesian framework for analyzing large spatial datasets.
• To introduce a novel "divide-and-conquer" strategy for spatial process models.
• To enable full posterior predictive inference for outcomes and spatial surfaces.

Main Methods:

• Proposing Spatial Meta-Kriging (SMK), a divide-and-conquer Bayesian strategy.
• Partitioning data into subsets and analyzing each with a spatial process model.
• Combining posterior distributions from subsets for approximate global inference.

Main Results:

• SMK offers superior scalability by avoiding storage of the entire dataset on one processor.
• The method provides full posterior predictive inference at arbitrary locations.
• Demonstrated effectiveness with Gaussian processes, tapered Gaussian processes, simulations, and sea surface temperature data.

Conclusions:

• Spatial Meta-Kriging (SMK) is an intuitive, implementable, and scalable solution for large-scale geostatistical analysis.
• The approach facilitates robust spatial modeling and prediction without prohibitive computational costs.
• SMK enhances the analysis of complex spatial phenomena in various scientific domains.