Comparison of performances of plug-in spatial classification rules based on Bayesian and ML estimators

The problem of classifying a scalar Gaussian random field observation into one of two populations specified by a different parametric drifts and common covariance model is considered. The unknown drift and scale parameters are estimated using given a spatial training sample. This paper concerns classification procedures associated to a parametric plug-in Bayes Rule obtained by substituting the unknown parameters in the Bayes rule by their estimators. The Bayesian estimators are used for the particular prior distributions of the unknown parameters. A closed-form expression is derived for the actual risk associated to the aforementioned classification rule. An estimator of the expected risk based on the derived actual risk is used as a performance measure for the classifier incurred by the plug-in Bayes rule. A stationary Gaussian random field with an exponential covariance function sampled on a regular 2-dimensional lattice is used for the simulation experiment. A critical performance comparison between the plug-in Bayes Rule defined above and a one based on ML estimators is performed.