Chentsov's theorem explained

In information geometry, Chentsov's theorem states that the Fisher information metric is, up to rescaling, the unique Riemannian metric on a statistical manifold that is invariant under sufficient statistics.

The theorem is named after its inventor Nikolai Chentsov

See also

• Fisher information
• Sufficient statistic
• Information geometry

References

• N. N. Čencov (1981), Statistical Decision Rules and Optimal Inference, Translations of mathematical monographs; v. 53, American Mathematical Society, http://www.ams.org/books/mmono/053/
• Shun'ichi Amari, Hiroshi Nagaoka (2000) Methods of information geometry, Translations of mathematical monographs; v. 191, American Mathematical Society, http://www.ams.org/books/mmono/191/ (Theorem 2.6)
• 10.1007/s41884-018-0006-4. Chentsov's theorem for exponential families. 2018. Dowty. James G.. Information Geometry. 1. 1. 117-135. 1701.08895.
• Akio . Fujiwara . Hommage to Chentsov's theorem . Info. Geo. . 2022 . 7 . 79–98 . 10.1007/s41884-022-00077-7 . free .