Natural differentiable structures on statistical models and the Fisher metric
Differential Geometry
2023-02-14 v4 Probability
Statistics Theory
Statistics Theory
Abstract
In this paper I discuss the relation between the concept of the Fisher metric and the concept of differentiability of a family of probability measures. I compare the concepts of smooth statistical manifolds, differentiable families of measures, -integrable parameterized measure models, diffeological statistical models, differentiable measures, which arise in Information Geometry, mathematical statistics and measure theory, and discuss some related problems.
Keywords
Cite
@article{arxiv.2208.06539,
title = {Natural differentiable structures on statistical models and the Fisher metric},
author = {Hông Vân Lê},
journal= {arXiv preprint arXiv:2208.06539},
year = {2023}
}
Comments
22p. submitted version to Information Geometry