论文标题
贝叶斯空间中多元密度的正交分解及其与Copulas的联系
Orthogonal decomposition of multivariate densities in Bayes spaces and its connection with copulas
论文作者
论文摘要
最初设计的贝叶斯空间是为分布数据建模和分析提供的几何框架。最近已经揭示了可以利用这种方法来将双变量概率分布的正交分解为独立和相互作用部分。在本文中，通过使用希尔伯特空间理论对其进行重新启动，并使用Hoeffding-Sobol身份的分布类似物来开发多元扩展，从而为这些结果提供了新的见解。还提供了多元密度的结果分解与基于副群体的表示之间的连接。
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.
