Factorial Discriminant Analysis and Probabilistic Models

In this paper two main approaches to discriminant analysis are considered with respect to the use of either the probabilistic models or the factorial methods. It is shown that they tend to satisfy equivalent statistical criteria. A choice among several discriminant methods should take into account the a priori information on the population structure which determines the sampling sheme to be adopted. To this purpose, a distinction is made between probabilistic or factorial discriminant methods under the prospective hypothesis and probabilistic or factorial discriminant methods under the retrospective hypothesis. In the frame of prospective studies we consider the First Order Independence Model and the Non-Symmetric Factorial Discriminant Aanalysis; in the frame of retrospective studies the Null-Order Independence Model and the Baricentric Discriminant Analysis.