A1399
Title: Spline approximation of probability density functions in Bayes spaces
Authors: Jitka Machalova - Palacky University (Czech Republic) [presenting]
Abstract: Probability density functions represent relative rather than absolute information and therefore require a geometry respecting scale invariance and the unit-integral constraint. Bayes spaces provide a natural framework for such data. Spline approximation methods for probability densities based on the centered logratio transformation are presented, which maps densities into the zero-integral subspace of $L^2$. Histogram observations are transformed into clr coordinates and approximated using penalized splines. Particular attention is devoted to zero-integral spline representations, where the constraint is incorporated directly into the spline basis. The proposed framework provides flexible and interpretable smoothing of density-valued data while preserving their compositional structure. Extensions to periodic and bivariate density functions based on tensor-product spline constructions are also discussed.
