Abstract
AbstractChentsov’s theorem, which characterises Markov invariant Riemannian metric and affine connections of manifolds of probability distributions on finite sample spaces, is undoubtedly a cornerstone of information geometry. This article aims at providing a comprehensible survey of Chentsov’s theorem as well as its modest extensions to generic tensor fields and to parametric models comprising continuous probability densities on $${\mathbb R}^k$$
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k
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Funder
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computer Science Applications,Geometry and Topology,Statistics and Probability
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