Title: A Bayes space approach to the analysis of probability density functions
Authors: Alessandra Menafoglio - Politecnico di Milano (Italy) [presenting]
Abstract: In several studies elementary data are aggregated, and then represented through probability density functions (PDFs). For instance, in socio-economic contexts, the age of the population is often described through its distribution (i.e., a population pyramid), whereas, in environmental studies, the soil granularity is typically represented through a particle-size distribution. In all these cases the dataset consists of PDFs, whose proper statistical treatment is key to describe, model and predict the phenomenon under study. Statistical methods for the analysis of PDFs need to account for the infinite-dimensionality of the data, and their inherent constraints. We will discuss the Bayes space viewpoint to the analysis of PDFs, which combine the approaches of functional data analysis and compositional data analysis, through the foundational role of the generalized Aitchison geometry. In this framework, methods for dimensionality reduction, modeling and prediction will be illustrated, with application to studies of industrial and environmental interest.