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 mathematician Nikolai Chentsov, who proved it in his 1981 paper.
References
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)
- Dowty, James G. (2018). "Chentsov's theorem for exponential families". Information Geometry. 1 (1): 117-135. arXiv:1701.08895. doi:10.1007/s41884-018-0006-4.
- Fujiwara, Akio (2022). "Hommage to Chentsov's theorem". Info. Geo. 7: 79–98. doi:10.1007/s41884-022-00077-7.