

Preprint 43/2003
Monotone invariants and embeddings of statistical manifolds
Hông Vân Lê
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Submission date: 05. May. 2003
Pages: 45
published 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 / N. M. Chuong (ed.)
Hackensack, NJ : World Scientific, 2007. - P. 231 - 253
DOI number (of the published article): 10.1142/9789812770493_0012
Bibtex
MSC-Numbers: 35, 62
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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.