B0262
Title: Information geometry of ANOVA and transport on a finite state space
Authors: Giovanni Pistone - de Castro Statistics, Collegio Carlo Alberto (Italy) [presenting]
Abstract: Functional ANOVA (Analysis of variance) is known in statistics and system theory. It is a non-parametric orthogonal splitting of the vector space of square-integrable random variables. It is used to split the fibres of the affine bundle of couples of probability densities and Fisher's scores, the so-called statistical bundle, provided a product sample space is maintained. One of the factors in the splitting is the additive model, while the other factor is the transportation model with fixed marginals. In this setting, the information geometry gradient flow in the transport sub-model has a limit point that solves the Kantorovich problem.
