Geostatistical Fisher discriminant analysis

A geostatistical version of the classical Fisher rule (linear discriminant analysis) is presented. This method is applicable when a large dataset of multivariate observations is available within a domain split in several known subdomains, and it assumes that the variograms (or covariance functions) are comparable between subdomains, which only differ in the mean values of the available variables. The method consists on finding the eigen-decomposition of the matrix inv(W) B, where W is the matrix of sills of all direct- and cross-variograms, and B is the covariance matrix of the vectors of weighted means within each subdomain, obtained by generalized least squares. The method is used to map peat blanket occurrence in Northern Ireland, with data from the Tellus survey, which requires a minimal change to the general recipe: to use compositionally-compliant variogram tools and models, and work with log-ratio transformed data.