Orthogonal decomposition of multivariate densities in Bayes spaces and relation with their copula-based representation
Christian Genest, Karel Hron, Johanna Nešlehová · Journal of Multivariate Analysis · 2023
Bayes spaces were initially designed to provide a geometric framework for the modeling and analysis of distributional data. It has recently come to light that this methodology can be exploited to construct an orthogonal decomposition of bivariate probability densities into an independence and an interaction part. In this paper, new insights into these results are given by reformulating them using Hilbert space theory, and a multivariate extension is developed using a distributional analog of the Hoeffding–Sobol identity. A connection is also made between the resulting decomposition of a multivariate density and its copula-based representation.