Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

In the geosciences it is still uncommon to include measurement uncertainties into numerical analysis such as discriminant analysis. The implementation of uncertainties is not trivial because data sets in geosciences often present a compositional nature, e.g. they are given as concentrations, proportions, percentages or any other form of information about the relative abundance of a set of components forming a whole. For these data the respective uncertainties are nearly never considering their compositional nature. The uncertainties can be incorporated in discriminant analysis either by each measured variable, by each observation or by using the individual, cell-wise uncertainties (each observation has for each variable an individual uncertainty). Most DA methods incorporating uncertainties use the uncertainties as weights for the variables or observations of the data set. In contrast, the here proposed method uses uncertainties to calculate a better estimation of the group variances and group means, which then influence the decision rules of quadratic respectively linear discriminant algorithm. This methodological framework does not only allow to incorporate cell-wise uncertainties, but also would largely be valid if the information about the co-dependency between uncertainties within each observation is reported.