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

作者:Bauer Martin*; Bruveris Martins; Michor Peter W
来源:Bulletin of the London Mathematical Society, 2016, 48(3): 499-506.
DOI:10.1112/blms/bdw020

摘要

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.

  • 出版日期2016-6