Review: Nonstationary Spatial Modeling, with Emphasis on Process Convolution and Covariate Driven Approaches
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.