Workshop
Monotone invariants and embeddings of statistical manifolds
- H. Van Lè
Abstract
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 by Amari on the existence of embedding of exponential families and to the Lauritzen question on realization of statistical manifolds as statistical models.