Nonstationary 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 in order to obtain parameter estimates. For Gaussian data the necessary assumptions are mean- and covariance stationarity. While simple techniques are available to deal with violations of mean stationarity, the same is not true for covariance stationarity. In order to handle mean nonstationarity as well as covariance nonstationarity, we propose the modelling by spatially varying coefficients. This aproach not only yields more appropriate models for nonstationary 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