Uniqueness of the Fisher–Rao metric on the space of smooth densities

By Martin Bauer, Martins Bruveris, Peter W. Michor. 2014

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On a compact manifold without boundary of dimension greater than 1, every smooth weak Riemannian metric on the space of smooth positive probability densities that is invariant under the action of the diffeomorphism group is a multiple of the Fisher–Rao metric.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/09926f806c5f835ea777f631e7e749865892ebe0