Transversality Conditions for Geodesics on the Statistical Manifold of Multivariate Gaussian Distributions

Information and Divergence Measures

The present Special Issue of Entropy, entitled Information and Divergence Measures, covers various aspects and applications in the general area of Information and Divergence Measures [...].

A Simple Approximation Method for the Fisher-Rao Distance between Multivariate Normal Distributions

We present a simple method to approximate the Fisher-Rao distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating the Fisher-Rao distances between successive nearby normal distributions on the curves by the square roots of their Jeffreys divergences. We consider experimentally the linear interpolation curves in the ordinary, natural, and expectation parameterizations of the normal distributions, and compare these curves with a curve derived from the Calvo and Oller's isometric embedding of the Fisher-Rao d-variate normal manifold into the cone of (d+1)×(d+1) symmetric positive-definite matrices. We report on our experiments and assess the quality of our approximation technique by comparing the numerical approximations with both lower and upper bounds. Finally, we present several information-geometric properties of Calvo and Oller's isometric embedding.