Spatial data (data that are geographically referenced) are commonly encountered
in varied fields such as ecology, epidemiology, public health, and geoscience. We
consider practical issues with using linear Gaussian process models, which are
among the most popular models for analyzing spatial data. We summarize some
commonly used frequentist and Bayesian approaches for modeling spatial data via
Gaussian processes. In the Bayesian context we review some standard approaches
for selecting appropriate priors. We also compare estimation and prediction for
Gaussian process models via a simulation study and through an application of our
methods to a spatial data set used for studying crop epidemics. We conclude with
some practical recommendations based on our study.