Monotone invariants and embeddings of statistical manifolds

  • Hông Vân Lê (MPI MiS, Leipzig)
A3 01 (Sophus-Lie room)


In this note we prove certain necessary and sufficient conditions for the existence of embedding of statistical manifolds. In particular we prove that any smooth statistical manifold can be embedded into the space of all probability measures on a finite set. As a result we get positive answers to the question of Amari on the existence of embedding of exponential families and to the Lauritzen question on realization of statistical manifolds as statistical models.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail