Spatial discriminant analysis using covariates information

The analysis of spatially distributed observations implies a number of theoretical problems due to the multidirectional dependence among nearest sites. The presence of such a dependence often causes the standard statistical method, instead based on independence assumptions, to provide inefficient estimates or, even, to fail badly. This paper concerns the problem of discrimination and classification of spatial polytomous data. It extends the approach discussed by Alfò and Postiglione (1999) for binary observations to polytomous data, presents a discrimination function based on markovian automodels and suggests a natural solution to the resulting allocation problem through a Gibbs sampler based procedure. The proposed approach is contrasted with standard logistic discrimination and applied to a real data set consisting of a remote sensed image from Nebrodi mountains (Italy).