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arXiv · 1909.12677

When Shannon and Khinchin meet Shore and Johnson: equivalence of information theory and statistical inference axiomatics

Petr Jizba·Jan Korbel
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Abstract

We propose a unified framework for both Shannon-Khinchin and Shore-Johnson axiomatic systems. We do it by rephrasing Shannon-Khinchine axioms in terms of generalized arithmetics of Kolmogorov and Nagumo. We prove that the two axiomatic schemes yield identical classes of entropic functionals -- Uffink class of entropies. This allows to re-establish the entropic parallelism between information theory and statistical inference that has seemed to be "broken" by the use of non-Shannonian entropies.

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BibTeXRIS

Petr Jizba, Jan Korbel. 2019-09-27. When Shannon and Khinchin meet Shore and Johnson: equivalence of information theory and statistical inference axiomatics. https://doi.org/10.1103/physreve.101.042126

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