Nonadditive entropies yield probability distributions with biases not warranted by the data

Steve Presse, Kingshuk Ghosh, Julian Lee, Ken A. Dill

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann-Gibbs form of the entropy ensures that probability distributions inferred satisfy the multiplication rule of probability for independent events in the absence of data coupling such events. Other types of entropies that violate the Shore and Johnson axioms, including nonadditive entropies such as the Tsallis entropy, violate this basic consistency requirement. Here we use the axiomatic framework of Shore and Johnson to show how such nonadditive entropy functions generate biases in probability distributions that are not warranted by the underlying data.

Original languageEnglish (US)
Article number180604
JournalPhysical Review Letters
Volume111
Issue number18
DOIs
StatePublished - Nov 1 2013
Externally publishedYes

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entropy
variational principles
axioms
multiplication
requirements

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Nonadditive entropies yield probability distributions with biases not warranted by the data. / Presse, Steve; Ghosh, Kingshuk; Lee, Julian; Dill, Ken A.

In: Physical Review Letters, Vol. 111, No. 18, 180604, 01.11.2013.

Research output: Contribution to journalArticle

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