Displaying similar documents to “A note on characterizations of entropies”

Canonical distributions and phase transitions

K.B. Athreya, J.D.H. Smith (2000)

Discussiones Mathematicae Probability and Statistics

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Entropy maximization subject to known expected values is extended to the case where the random variables involved may take on positive infinite values. As a result, an arbitrary probability distribution on a finite set may be realized as a canonical distribution. The Rényi entropy of the distribution arises as a natural by-product of this realization. Starting with the uniform distributionon a proper subset of a set, the canonical distribution of equilibriumstatistical mechanics may...

Entropy of probability kernels from the backward tail boundary

Tim Austin (2015)

Studia Mathematica

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A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space (X,μ). These works have culminated in a proof by Downarowicz and Frej that various competing definitions all coincide, and that the resulting quantity is uniquely characterized by certain abstract properties. On the other hand, Makarov has shown that this...

A pragmatic uncertainty measure based on rate-distortion theory and the uncertainty of BOE's.

Anna Fioretto, Andrea Sgarro (1996)

Mathware and Soft Computing

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We discuss pragmatic information measures (hypergraph entropy and fractional entropy) inspired by source-coding theory (rate-distortion theory). We re-phrase the problem in the language of evidence theory, by expressing the pragmatic requirements of the human agent in terms of suitable bodies of evidence, or BOE's. We tackle the situation when the overall uncertainty is removed in two steps. In the case when fractional entropy measures the first-step (partial, pragmatic) uncertainty,...