B1068
Title: Principal component analysis in Bayes spaces for sparsely sampled density functions
Authors: Lisa Steyer - Humboldt University of Berlin (Germany)
Sonja Greven - Humboldt University of Berlin (Germany) [presenting]
Abstract: A novel approach is presented to functional principal component analysis (FPCA) in Bayes spaces in the setting where densities are the object of analysis, but only a few individual samples from each density are observed. The observed data is used directly to account for all sources of uncertainty, instead of relying on prior estimation of the underlying densities in a two-step approach, which can be inaccurate if small or heterogeneous numbers of samples per density are available. To account for the constrained nature of densities, the approach is based on Bayes spaces, which extend the Aitchison geometry for compositional data to density functions. For modeling, the isometric isomorphism is exploited between the Bayes space and the L2 subspace $L2_0$ with integration-to-zero constraint through the centered log-ratio transformation. As only discrete draws from each density are observed, the underlying functional densities are treated as latent variables within a maximum likelihood framework and employ a Monte Carlo expectation maximization (MCEM) algorithm for model estimation. The proposed method is applied to analyze the distribution of daily rainfall over different years.
