Information geometry of Bayes computations

Abstract

Amari's Information Geometry is a dually affine formalism for parametric probability models. The literature proposes various nonparametric functional versions. Our approach uses classical Weyl's axioms so that the affine velocity of a one-parameter statistical model equals the classical Fisher's score. In the present note, we first offer a concise review of the notion of a statistical bundle as a set of couples of probability densities and Fisher's scores. Then, we show how the nonparametric dually affine setup deals with the basic Bayes and Kullback-Leibler divergence computations.