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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
43/2003

Monotone invariants and embeddings of statistical manifolds

Hông Vân Lê

Abstract

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.

Received:
May 5, 2003
Published:
May 5, 2003
MSC Codes:
35, 62

Related publications

inBook
2007 Repository Open Access
Hông Vân Lê

Monotone invariants and embeddings of statistical manifolds

In: Advances in deterministic and stochastic analysis : proceedings of the 2nd international conference on abstract and applied analysis, Quy Nhon, Vietnam, June 4-9. 2005 / Ngyuen Minh Chuong (ed.)
Hackensack, NJ : World Scientific, 2007. - pp. 231-253