Fisher-Rao Geometry Of Dirichlet Distributions

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 a Hadamard manifold, i.e. that it is geodesically complete and has everywhere negative sectional curvature. An important consequence for applications is that the Frechet mean of a set of Dirichlet distributions is uniquely defined in this geometry. (C) 2020 Elsevier B.V. All rights reserved.