Premium
Uniqueness of the Fisher–Rao metric on the space of smooth densities
Author(s) -
Bauer Martin,
Bruveris Martins,
Michor Peter W.
Publication year - 2016
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdw020
Subject(s) - mathematics , diffeomorphism , fisher information metric , statistical manifold , riemannian manifold , metric (unit) , uniqueness , pure mathematics , boundary (topology) , mathematical analysis , invariant (physics) , manifold (fluid mechanics) , metric space , space (punctuation) , information geometry , injective metric space , scalar curvature , geometry , mathematical physics , curvature , linguistics , operations management , philosophy , economics , mechanical engineering , engineering
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.