Chentsov’s theorem for exponential families

  title={Chentsov’s theorem for exponential families},
  author={James G. Dowty},
  journal={Information Geometry},
  • J. Dowty
  • Published 2017
  • Mathematics, Computer Science
  • Information Geometry
Chentsov’s theorem characterizes the Fisher information metric on statistical models as the only Riemannian metric (up to rescaling) that is invariant under sufficient statistics. This implies that each statistical model is equipped with a natural geometry, so Chentsov’s theorem explains why many statistical properties can be described in geometric terms. However, despite being one of the foundational theorems of statistics, Chentsov’s theorem has only been proved previously in very restricted… Expand
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