Information Geometry and Statistical Manifold

TL;DR

This paper reviews fundamental concepts in information geometry, including Fisher metric and $ abla^{(eta)}$-connections, and discusses their application to asymptotic statistical inference, highlighting the geometric structure of statistical models.

Contribution

It provides a comprehensive overview of information geometry concepts and demonstrates their application to asymptotic statistical inference, connecting geometric structures with statistical analysis.

Findings

Fisher metric defines a Riemannian structure on statistical manifolds.

$ abla^{(eta)}$-connections describe affine structures related to statistical divergence.

Application to asymptotic inference illustrates the practical relevance of geometric methods.

Abstract

We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, $\alpha$-connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic statistical inference.