Monotone invariants and embeddings of statistical manifolds

Details Monotone invariants and embeddings of statistical manifolds Monotone invariants and embeddings of statistical manifolds

2005-06-09

arxiv.org/abs/math/0506163v3

in the book "Advances in Deterministic and Stochastic Analysis", World Scientific, 2007, 231-254

Mathematics

Differential Geometry

misprints are corrected, Remark 5.26 is added

Scientific paper

In this note we prove certain necessary and sufficient conditions for the existence of an embedding of statistical manifolds. In particular, we prove that any smooth ($C^1$ resp.) statistical manifold can be embedded into the space of probability measures on a finite set. As a result, we get positive answers to the Lauritzen question on a realization of smooth ($C^1$ resp.) statistical manifolds as statistical models

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