  An explicit optimal linear spatial predictor is derived. The spatial
correlations are imposed by means of Gibbs energy functionals with explicit
coupling coefficients instead of covariance matrices. The model inference
process is based on physically identifiable constraints corresponding to
distinct terms of the energy functional. The proposed predictor is compared
with the geostatistical linear optimal filter (kriging) using simulated data.
The agreement between the two methods is excellent. The proposed framework
allows a unified approach to the problems of parameter inference, spatial
prediction and simulation of spatial random fields.
