Fisher-Rao geometry of Dirichlet distributions
Differential Geometry
2020-11-20 v2 Statistics Theory
Statistics Theory
Abstract
In this paper, we study the geometry induced by the Fisher-Rao metric on the parameter space of Dirichlet distributions. We show that this space is geodesically complete and has everywhere negative sectional curvature. An important consequence of this negative curvature for applications is that the Fr{\'e}chet mean of a set of Dirichlet distributions is uniquely defined in this geometry.
Keywords
Cite
@article{arxiv.2005.05608,
title = {Fisher-Rao geometry of Dirichlet distributions},
author = {Alice Le Brigant and Stephen Preston and Stéphane Puechmorel},
journal= {arXiv preprint arXiv:2005.05608},
year = {2020}
}