On bounds for the Fisher-Rao distance between multivariate normal distributions

Abstract

Information geometry is approached here by considering the statistical model of multivariate normal distributions as a Riemannian manifold with the natural metric provided by the Fisher information matrix. Explicit forms for the Fisher-Rao distance associated to this metric and for the geodesics of general distribution models are usually very hard to determine. In the case of general multivariate normal distributions lower and upper bounds have been derived. We approach here some of these bounds and introduce a new one discussing their tightness in specific cases.