Supervised Classification of the Scalar Gaussian Random Field Observations under a Deterministic Spatial Sampling Design

Given training sample, the problem of classifying a scalar Gaussian random field observation into one of two populations specified by different parametric mean models and common parametric covariance function is considered. Such problems are usually called as supervised classification or contextual classification problems. This paper concerns with classification procedures associated with Bayes Discriminant Function (BDF) under deterministic spatial sampling design. In the case of parametric uncertainty, the ML estimators of unknown parameters are plugged in the BDF. The actual risk and the approximation of the expected risk (AER) associated with aforementioned plug-in BDF are derived. This is the extension of the previous one to the case of complete parametric uncertainty, i.e., when all mean functions and covariance function parameters are unknown. Stationary geometrically anisotropic Gaussian random field with exponential covariance function sampled on regular 2-dimensional lattice is used for illustrative examples.