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

Published 20 Nov 2014 in math.DG and math.PR | (1411.5577v2)

Abstract: On a closed manifold of dimension greater than one, 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.

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