Application of Bayes Discriminant Functions to Classification of the Spatial Multivariate Gaussian Data

For given training sample, the problem of supervised classifying the multivariate stationary Gaussian random field (GRF) observations into one of two populations is considered. The populations are specified by different regression mean models and by common factorized covariance function. For completely specified populations the formula of Bayes error rate is derived. In the case of unknown regression parameters and covariance function parameters, the plug-in Bayes discriminant function based on ML estimators of parameters is used for spatial classification. The actual error rate and the asymptotic approximation of the expected error rate (AER) associated with plug-in Bayes discriminant function are derived. These results are multivariate generalization of previous one [1] for complete parametric uncertainty case. Numerical analysis of the derived formulas is implemented for the bivariate stationary GRF observations at locations belonging to the 2-dimensional lattice with unit spacing and exponential spatial correlation. Numerical comparison of two training label configurations (TLC) by the values of AER as optimality criterion is implemented.