With the collection of large amounts of data and the need to aggregate them into meaningful domains, there is an increasing interest in probability density functions (PDFs) as data objects and their statistical processing using functional data analysis (FDA) methods. When PDFs are embedded as scale-invariant positive functions in Bayes space with Hilbert space structure, it is possible to analyse them with popular methods of FDA due to isometric isomorphism with L2 space. Moreover, if the PDFs are multivariate, it is possible to decompose them orthogonally into independent and interactive parts, the latter capturing interactions between all possible combinations of variables. The key aspect here is the appropriate reformulation of the marginals into so-called geometric marginals, which are orthogonal projections of the multivariate information contained in the distribution into the univariate case. In this paper we focus on discussing the role and interpretation of geometric marginals and highlight their main implications.

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Multivariate Densities in Bayes Spaces: The Novel Concept of Marginals and Its Implications

  • Karel Hron

摘要

With the collection of large amounts of data and the need to aggregate them into meaningful domains, there is an increasing interest in probability density functions (PDFs) as data objects and their statistical processing using functional data analysis (FDA) methods. When PDFs are embedded as scale-invariant positive functions in Bayes space with Hilbert space structure, it is possible to analyse them with popular methods of FDA due to isometric isomorphism with L2 space. Moreover, if the PDFs are multivariate, it is possible to decompose them orthogonally into independent and interactive parts, the latter capturing interactions between all possible combinations of variables. The key aspect here is the appropriate reformulation of the marginals into so-called geometric marginals, which are orthogonal projections of the multivariate information contained in the distribution into the univariate case. In this paper we focus on discussing the role and interpretation of geometric marginals and highlight their main implications.