An extended Čencov characterization of the information metric

Author:
L. L. Campbell

Journal:
Proc. Amer. Math. Soc. **98** (1986), 135-141

MSC:
Primary 62B10; Secondary 53B99

DOI:
https://doi.org/10.1090/S0002-9939-1986-0848890-5

MathSciNet review:
848890

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Abstract | References | Similar Articles | Additional Information

Abstract: Čencov has shown that Riemannian metrics which are derived from the Fisher information matrix are the only metrics which preserve inner products under certain probabilistically important mappings. In Čencov's theorem, the underlying differentiable manifold is the probability simplex . For some purposes of using geometry to obtain insights about probability, it is more convenient to regard the simplex as a hypersurface in the positive cone. In the present paper Čencov's result is extended to the positive cone. The proof uses standard techniques of differential geometry but does not use the language of category theory.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0848890-5

Keywords:
Information metric,
Markov mapping

Article copyright:
© Copyright 1986
American Mathematical Society