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 provide an orthogonal decomposition of bivariate probability distributions into an independent and an interaction part. In this paper, new insights into these results are provided by reformulating them using Hilbert space theory and a multivariate extension is developed using a distributional analog of the Hoeffding-Sobol identity. A connection between the resulting decomposition of a multivariate density and its copula-based representation is also provided.
翻译:Bayes空间最初设计为分配数据的建模和分析提供一个几何框架,最近人们发现,这一方法可以用来提供两变概率分布的正对分解成一个独立的互动部分,本文件通过使用Hilbert空间理论重新校正这些结果,对这些结果有了新的了解,并利用Hoffding-Sobol特性的分布类比,开发了多变扩展,并提供了多变密度的分解及其以千叶为基的表示方式之间的联系。