A0178
Title: Density data analysis for densities observed via samples
Authors: Sonja Greven - Humboldt University of Berlin (Germany) [presenting]
Abstract: In density data analysis, densities are in many settings the objects of interest and analysis, but are latent and only observed via samples. Common two-step approaches then first reconstruct densities using methods such as kernel density estimation or (compositional) splines, and ignore estimation uncertainty in the subsequent density data analysis. However, these approaches can be inaccurate, particularly if small or heterogeneous numbers of samples per density are available. The aim is to propose modeling individual draws from latent densities directly to incorporate all sources of uncertainty. This approach is illustrated for the cases of density principal component analysis as well as regression with densities as outcomes or covariates. To account for the constrained nature of densities, we base our approaches on Bayes spaces, which extend the Aitchison geometry for compositional data (discrete densities) to more general densities. Estimation can be based on (penalized) maximum likelihood estimation, in some cases requiring a (Monte Carlo) expectation maximization algorithm to handle latent densities. All approaches are illustrated with applications ranging from gender economics to climate research.
