  A new orthogonal decomposition for bivariate probability densities embedded
in Bayes Hilbert spaces is derived. It allows one to represent a density into
independent and interactive parts, the former being built as the product of
revised definitions of marginal densities and the latter capturing the
dependence between the two random variables being studied. The developed
framework opens new perspectives for dependence modelling (which is commonly
performed through copulas), and allows for the analysis of dataset of bivariate
densities, in a Functional Data Analysis perspective. A spline representation
for bivariate densities is also proposed, providing a computational cornerstone
for the developed theory.
