Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Regression Framework

TL;DR

This paper introduces a conjugate Bayesian linear regression framework for large-scale spatial datasets, enabling fast, exact inference without iterative algorithms, suitable for practical spatial analysis in GIS.

Contribution

It presents a novel conjugate Bayesian approach for scalable spatial modeling that simplifies implementation and speeds up inference compared to existing methods.

Findings

Enables exact sampling from the joint posterior distribution.

Eliminates the need for iterative algorithms like MCMC.

Facilitates easy implementation in standard statistical software.

Abstract

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.