  In many environmental applications involving spatially-referenced data,
limitations on the number and locations of observations motivate the need for
practical and efficient models for spatial interpolation, or kriging. A key
component of models for continuously-indexed spatial data is the covariance
function, which is traditionally assumed to belong to a parametric class of
stationary models. While convenient, the assumption of stationarity is rarely
realistic; as a result, there is a rich literature on alternative methodologies
which capture and model the nonstationarity present in most environmental
processes. This review document provides a rigorous and concise description of
the existing literature on nonstationary methods, paying particular attention
to process convolution (also called kernel smoothing or moving average)
approaches. A summary is also provided of more recent methods which leverage
covariate information and yield both interpretational and computational
benefits.
  Note: the article is borrowed from Chapters 1 and 2 of the author's Ph.D.
dissertation, joint with Catherine A. Calder.
