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.