Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Regression Framework
This provides an easily implementable solution for practicing scientists and spatial analysts dealing with massive spatial data, though it is incremental as it builds on existing spatial process models.
The paper tackles the challenge of scalable Bayesian inference for large spatial datasets by proposing a conjugate Bayesian linear regression framework that enables exact sampling from posterior distributions, avoiding iterative MCMC methods and allowing rapid implementation in environments like R.
Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models have been proposed that can be easily embedded within a hierarchical modeling framework to carry out Bayesian inference. While the focus of statistical research has mostly been directed toward innovative and more complex model development, relatively limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article discusses how point-referenced spatial process models can be cast as a conjugate Bayesian linear regression that can rapidly deliver inference on spatial processes. The approach allows exact sampling directly (avoids iterative algorithms such as Markov chain Monte Carlo) from the joint posterior distribution of regression parameters, the latent process and the predictive random variables, and can be easily implemented on statistical programming environments such as R.