Orthogonal decomposition of multivariate densities in Bayes spaces and relation with their copula-based representation
本文利用Hilbert空间理论重新表述了贝叶斯空间中二元密度的正交分解，并将其扩展到多元情形，同时建立了该分解与Copula表示之间的联系。
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.