Uniqueness of the Fisher–Rao metric on the space of smooth densities
Copyright policy )Uniqueness of the Fisher–Rao metric on the space of smooth densities
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.
8 pages. This version: Main theorem reformulated, small changes
- Brunel University London United Kingdom
- University of Vienna Austria
- TU Wien Austria
Manifolds of mappings, Mathematics - Differential Geometry, information geometry, space of densities, 101024 Wahrscheinlichkeitstheorie, Invariant Metrics, 58B20, 58D15, 370, groups of diffeomorphisms, 101002 Analysis, 101006 Differentialgeometrie, 510, Groups of Diffeomorphisms, 101006 Differential geometry, Fisher–Rao metric, FOS: Mathematics, 101024 Probability theory, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, Fisher–Rao Metric, Information Geometry, 660, Probability (math.PR), spaces of smooth positive probability densities, Fisher-Rao metric in information geometry, Differential Geometry (math.DG), Space of Densities, invariant metrics, Mathematics - Probability
Manifolds of mappings, Mathematics - Differential Geometry, information geometry, space of densities, 101024 Wahrscheinlichkeitstheorie, Invariant Metrics, 58B20, 58D15, 370, groups of diffeomorphisms, 101002 Analysis, 101006 Differentialgeometrie, 510, Groups of Diffeomorphisms, 101006 Differential geometry, Fisher–Rao metric, FOS: Mathematics, 101024 Probability theory, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, Fisher–Rao Metric, Information Geometry, 660, Probability (math.PR), spaces of smooth positive probability densities, Fisher-Rao metric in information geometry, Differential Geometry (math.DG), Space of Densities, invariant metrics, Mathematics - Probability
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