Displaying similar documents to “$(R,S)$-information radius of type $t$ and comparison of experiments”

Notion of information and independent component analysis

Una Radojičić, Klaus Nordhausen, Hannu Oja (2020)

Applications of Mathematics

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Partial orderings and measures of information for continuous univariate random variables with special roles of Gaussian and uniform distributions are discussed. The information measures and measures of non-Gaussianity including the third and fourth cumulants are generally used as projection indices in the projection pursuit approach for the independent component analysis. The connections between information, non-Gaussianity and statistical independence in the context of independent component...

On generalized information and divergence measures and their applications: a brief review.

Inder Jeet Taneja, Leandro Pardo, Domingo Morales, María Luisa Menéndez (1989)

Qüestiió

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The aim of this review is to give different two-parametric generalizations of the following measures: directed divergence (Kullback and Leibler, 1951), Jensen difference divergence (Burbea and Rao 1982 a,b; Rao, 1982) and Jeffreys invariant divergence (Jeffreys, 1946). These generalizations are put in the unified expression and their properties are studied. The applications of generalized information and divergence measures to comparison of experiments and the connections with Fisher...

Physical measures for infinite-modal maps

Vítor Araújo, Maria José Pacifico (2009)

Fundamenta Mathematicae

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We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they...

A note on the interval-valued marginal problem and its maximum entropy solution

Jiřina Vejnarová (1998)

Kybernetika

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This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of...

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,...