Spatial statistics and Gaussian processes: A beautiful marriage

Spatial analysis has grown at a remarkable rate over the past two decades. Fueled by sophisticated GIS software and inexpensive and fast computation, collection of data with spatially referenced information has increased. Recognizing that such information can improve data analysis has led to an explosion of modeling and model fitting.The contribution of this paper is to illustrate how Gaussian processes have emerged as, arguably, the most valuable tool in the toolkit for geostatistical modeling. Apart from the simplest versions, geostatistical modeling can be viewed as a hierarchical specification with Gaussian processes introduced appropriately at different levels of the specification. This naturally leads to adopting a Bayesian framework for inference and suitable Gibbs sampling/Markov chain Monte Carlo for model fitting.Here, we review twenty years of modeling work spanning multivariate spatial analysis, gradient analysis, Bayesian nonparametric spatial ideas, directional data, extremes, data fusion, and large spatial and spatio-temporal datasets. We demonstrate that Gaussian processes are the key ingredients in all of this work. Most of the content is focused on modeling with examples being limited due to length constraints for the article. Altogether, we are able to conclude that spatial statistics and Gaussian processes do, indeed, make a beautiful marriage.