Monotone invariants and embeddings of statistical manifolds
Hông Vân Lê
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Submission date: 05. May. 2003
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
MSC-Numbers: 35, 62
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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.