A1247
Title: A semiparametric approach to multivariate density decomposition in Bayes spaces
Authors: Karel Hron - Palacky University (Czech Republic) [presenting]
Johanna Neslehova - McGill University (Canada)
Christian Genest - McGill University (Canada)
Adela Czolkova - Palacky University Olomouc (Czech Republic)
Ondrej Ulicny - Palacky University Olomouc (Czechia)
Abstract: Multivariate probability density functions with square-integrable logarithms can be represented within Bayes spaces, where they can be decomposed into mutually orthogonal components capturing main effects and interactions. While this formulation is theoretically attractive, fully nonparametric estimation of such densities becomes impractical in higher-dimensional settings. A semiparametric approach based on a truncated multivariate normal distribution addresses this challenge. Within this framework, both the density and its corresponding information composition can be expressed explicitly through the precision matrix. This greatly facilitates maximum likelihood estimation of multivariate densities and supports the analysis of information compositions using established multivariate methods, such as principal component analysis, hierarchical clustering, and regression analysis, adapted to an interpretable log-ratio representation. Depending on the setting, the approach has potential utility for investigating complex dependence structures in multivariate density data.
