Expected Bayes Error Rate in Supervised Classification of Spatial Gaussian Data

In the usual statistical approach of spatial classification, it is assumed that the feature observations are independent conditionally on class labels (conditional independence). Discarding this popular assumption, we consider the problem of statistical classification by using multivariate stationary Gaussian Random Field (GRF) for modeling the conditional distribution given class labels of feature observations. The classes are specified by multivariate regression model for means and by common factorized covariance function. In the two-class case and for the class labels modeled by Random Field (RF) based on 0–1 divergence, the formula of the Expected Bayes Error Rate (EBER) is derived. The effect of training sample size on the EBER and the influence of statistical parameters to the values of EBER are numerically evaluated in the case when the spatial framework of data is the subset of the 2-dimensional rectangular lattice with unit spacing.