Discrimination Based on an Odds Ratio Parameterization

It is argued that the association of any two random elements with positive joint probability density function is characterized by its odds ratio function. The impact of this fundamental result is explored in two applications. In Bayesian analyses it is the association between an observable random variable and a random parameter that is of primary interest. In multivariate analysis it is the association between two random vectors that is investigated. If two random elements are strongly related the corresponding conditional distributions can well be separated. A concept of dependence therefore implies an approach to solving problems of discrimination. Discrimination based on the characterization of association by the odds ratio function is exemplified in Bayesian inference and in multivariate analysis.