Hommage to Chentsov’s theorem

Abstract

Chentsov’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 Rk.