Fisher-Rao distance on the covariance cone

Joseph Wells, Mary Cook, Karleigh Pine, Benjamin D. Robinson

Published 2020-10-29Version 1

The Fisher-Rao geodesic distance on the statistical manifold consisting of zero-mean p-dimensional multivariate Gaussians appears without proof in several places (such as Steven Smith's "Covariance, Subspace, and Intrinsic Cramer-Rao Bounds"). In this paper, we give a proof using basic Riemannian geometry.