Understanding Bayes spaces

J. J. Egozcue - V. Pawlowsky-Glahn
U. Politecnica de Catalunya, Barcelona, Spain --- Univ. de Girona, Girona, Spain
Tuesday 31st March 2015
Aula Saleri VI piano del Dipartimento di Matematica - MOX - Politecnico di Milano
Bayes spaces contain equivalence classes of -additive measures. Two measures are equivalent when they are proportional. These measures are represented by densities and vector space operations are dened. Probability measures and density functions are included in these spaces. When the densities are log-square-integrable, they are in a Hilbert space called B2. Bayes spaces and associated Hilbert spaces B2 have been developed in a theoretical way, but there is still a long way to understand the implications of the theory, as well as to develop potential applications. The talk is aimed at reviewing the theory and giving some examples of distributions for which the B2 distance can be easily obtained. These examples show the variety of distribution supports that can be dealt with the theory. An application to grain size distribution is presented. The goal is to decide whether different populations have different mean distribution. contact: piercesare.secchi@polimi.it --- laura.sangalli@polimi.it