Error rates in classification of multivariate Gaussian random field observation

We consider the problem of supervised classifying the multivariate Gaussian random field (GRF) single observation into one of two populations in case of given training sample. The populations are specified by different regression mean models and by common factorized covariance function. For completely specified populations, we derive a formula for Bayes error rate. In the case of unknown regression parameters and feature covariance matrix, the plug-in Bayes discriminant function based on ML estimators of parameters is used for classification. We derive the actual error rate and the asymptotic expansion of the expected error rate associated with plug-in Bayes discriminant function. These results are multivariate generalizations of previous ones. Numerical analysis of the derived formulas is implemented for the bivariate GRF observations at locations belonging to the two-dimensional lattice with unit spacing.