Error rates in multi-category classification of the spatial multivariate Gaussian data

The problem of classifying a spatial multivariate Gaussian data into one of several categories specified by different regression mean models is considered. The classifier based on plug-in Bayes classification rule (PBCR) formed by replacing unknown parameters in Bayes classification rule (BCR) with category parameters estimators is investigated. This is the extension of the previous one from the two category case to the multiple category case. The novel close-form expressions for the Bayes misclassification probability and actual error rate associated with PBCR are derived. These error rates are suggested as performance measures for the classifications procedure. The three-category case with feature modelled by bivariate stationary Gaussian random field on regular lattice with exponential covariance function is used for the numerical analysis. Dependence of the derived error rates on category parameters is studied.