Non-stationary conditional models for spatial data based on varying coefficients

The analysis of spatial data by means of Markov random fields usually is based on strict stationarity assumptions. Although these assumptions rarely hold, they are necessary for standard estimation methods to work. The assumptions required for Gaussian spatial data are mean and covariance stationarity. Whereas simple techniques are available to deal with violations of mean stationarity, the same is not true for covariance stationarity. To handle mean non-stationarity as well as covariance non-stationarity, we propose modelling by spatially varying coefficients. This approach not only yields more appropriate models for non-stationary data but also can be used to detect violations of the stationarity assumptions. The method is illustrated by use of the well-known wheat yield data.