论文标题
贝叶斯空间中的双变量密度：正交分解和样条表示
Bivariate Densities in Bayes Spaces: Orthogonal Decomposition and Spline Representation
论文作者
论文摘要
得出了一种新的嵌入贝叶斯河位空间中的双变量概率密度的正交分解。它允许一个人表示密度为独立和交互零件，前者被构建为边际密度的修订定义的产物，后者捕获了研究的两个随机变量之间的依赖性。开发的框架为依赖模型（通常是通过Copulas执行）打开了新的观点，并允许通过功能数据分析的角度来分析双变量密度数据集。还提出了双变量密度的样条表示，为开发理论提供了一个计算基石。
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.
