The approaches to model covariance non-stationarity can be classified coarsely into global and local methods. A global method considers the entire domain, a local method assumes that a globally non-stationarity process can be represented as a combination of locally stationary processes. The predictor that excludes observed sites is no longer best and the analyst must decide on the size and shape of the kriging neighborhood. Constructing non-stationary processes from convolutions is an elegant and powerful approach with great promise. The method of weighted stationary processes is closely related to convolution methods and many models in this class have a convolution representation. The important difference between this and the previously discussed approach is the assumption about which model component is spatially evolving.