### 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 language | English (US) |
---|---|

Article number | 180604 |

Journal | Physical Review Letters |

Volume | 111 |

Issue number | 18 |

DOIs | |

State | Published - Nov 1 2013 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*111*(18), [180604]. https://doi.org/10.1103/PhysRevLett.111.180604

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

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 111, no. 18, 180604. https://doi.org/10.1103/PhysRevLett.111.180604

}

TY - JOUR

T1 - Nonadditive entropies yield probability distributions with biases not warranted by the data

AU - Presse, Steve

AU - Ghosh, Kingshuk

AU - Lee, Julian

AU - Dill, Ken A.

PY - 2013/11/1

Y1 - 2013/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84887115648&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887115648&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.111.180604

DO - 10.1103/PhysRevLett.111.180604

M3 - Article

VL - 111

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 18

M1 - 180604

ER -