  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.
