Multiclass classification of the scalar Gaussian random field observation with known spatial correlation function

Given training sample, the problem of classifying the scalar Gaussian random field observation into one of several classes specified by different regression mean models and common parametric covariance function is considered. The classifier based on the plug-in Bayes classification rule formed by replacing unknown parameters in Bayes classification rule with their ML estimators is investigated. This is the extension of the previous one from the two-class case to the multiclass case. The novel close form expressions for the actual error rate and approximation of the expected error rate incurred by proposed classifier are derived. These error rates are suggested as performance measures for the proposed classifier. The three-class case with feature modelled by scalar stationary Gaussian random field on regular lattice with exponential covariance function is used for the numerical analysis of the proposed classifier performance. The accuracy of the obtained approximation is checked through a simulation study for various parametric structure cases.