Applied Geospatial Bayesian Modeling in the Big Data Era: Challenges and Solutions

Abstract

Two important trends in applied statistics are an increased usage of geospatial models and an increased usage of big data. Naturally, there has been overlap as analysts utilize the techniques associated with each. With geospatial methods such as kriging, the computation required becomes intensive quickly, even with datasets that would not be considered huge in other contexts. In this work we describe a solution to the computational problem of estimating Bayesian kriging models with big data, Bootstrap Random Spatial Sampling (BRSS), and first provide an analytical argument that BRSS produces consistent estimates from the Bayesian spatial model. Second, with a medium-sized dataset on fracking in West Virginia, we show that bootstrap sample effects from a full-information Bayesian model are reduced with more bootstrap samples and more observations per sample as in standard bootstrapping. Third, we offer a realistic illustration of the method by analyzing campaign donors in California with a large geocoded dataset. With this solution, scholars will not be constrained in their ability to apply theoretically relevant geospatial Bayesian models when the size of the data produces computational intractability.

Keywords

• Bayesian kriging
• bootstrap
• spatial modeling
• big data
• spatial quantiles
• smoothing