Foundations of Structural Statistics: Statistical Manifolds
Statistics Theory
2020-06-23 v2 Information Theory
math.IT
Statistics Theory
Abstract
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices, which in the category of statistical models are induced by statistical divergences. The present article extends the notation of topological statistical models by a differential structure to statistical manifolds and introduces the differential geometric foundations to study distribution families by their differential-, Riemannian- and symplectic geometry.
Cite
@article{arxiv.2002.07424,
title = {Foundations of Structural Statistics: Statistical Manifolds},
author = {Patrick Michl},
journal= {arXiv preprint arXiv:2002.07424},
year = {2020}
}