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Monotone invariants and embeddings of statistical manifolds

Hong-Van Le
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Abstract

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 compact smooth ($C^1$ resp.) statistical manifold can be embedded into the space of probability measures on a finite set. As a result, we get an answer to the Lauritzen question on a realization of smooth ($C^1$ resp.) statistical manifolds as statistical models

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Hong-Van Le. 2016-03-10. Monotone invariants and embeddings of statistical manifolds. https://arxiv.org/abs/math/0506163

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