A Lecture About the Use of Orlicz Spaces in Information Geometry

TL;DR

This paper provides a tutorial on the application of Orlicz spaces within information geometry, covering theoretical foundations and advanced functional spaces relevant to statistical models.

Contribution

It introduces the use of exponential and Gaussian Orlicz spaces in non-parametric information geometry, expanding the mathematical toolkit for statistical analysis.

Findings

Detailed exposition of Orlicz spaces in information geometry

Connections between Orlicz spaces and statistical bundles

Potential applications in non-parametric statistical models

Abstract

This is a revised version of a tutorial lecture that I presented at the \`Ecole de Physique des Houches on July 26-31 2020. Topics include Non-parametric Information Geometry, the Statistical bundle, exponential Orlicz spaces, and Gaussian Orlicz-Sobolev spaces.