A0209
Title: Orthogonal decomposition of multivariate densities in Bayes spaces in context of functional data analysis
Authors: Karel Hron - Palacky University (Czech Republic) [presenting]
Christian Genest - McGill University (Canada)
Johanna Neslehova - McGill University (Canada)
Abstract: Probability density functions can be embedded in the geometric framework of Bayes spaces which respect their relative nature and enable further modeling and analysis. Specifically, the Hilbert space structure of Bayes spaces has several important implications for estimation theory, Bayesian statistics as well as functional data analysis. In this contribution, an orthogonal decomposition of multivariate densities in Bayes spaces using a distributional analog of the HoeffdingSobol identity is constructed. The decomposition is based on reformulation of the standard (arithmetic) marginals to so-called geometric marginals, which are orthogonal projections of the univariate information contained in multivariate densities, follow the Yule perturbation and coincide with the arithmetic ones in case of independence. Accordingly, the decomposition contains an independent part and all possible interaction terms. The orthogonality of the decomposition results in Pythagoras' Theorem for squared norms of the decomposed densities and margin-free property of the interaction terms. There is also a relation between copula-based representation of densities and their functional data analysis. The latter will be illustrated with empirical geochemical data.
