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Limits of Bayesian decision related quantities of binomial asset price models

Wolfgang Stummer, Wei Lao (2012)

Kybernetika

We study Bayesian decision making based on observations X n , t : t ∈ { 0 , T n , 2 T n , ... , n T n } ( T > 0 , n ∈ ℕ ) of the discrete-time price dynamics of a financial asset, when the hypothesis a special n -period binomial model and the alternative is a different n -period binomial model. As the observation gaps tend to zero (i. e. n → ∞ ), we obtain the limits of the corresponding Bayes risk as well as of the related Hellinger integrals and power divergences. Furthermore, we also give an example for the “non-commutativity” between Bayesian statistical and...

Mean mutual information and symmetry breaking for finite random fields

J. Buzzi, L. Zambotti (2012)

Annales de l'I.H.P. Probabilités et statistiques

G. Edelman, O. Sporns and G. Tononi have introduced the neural complexity of a family of random variables, defining it as a specific average of mutual information over subfamilies. We show that their choice of weights satisfies two natural properties, namely invariance under permutations and additivity, and we call any functional satisfying these two properties an intricacy. We classify all intricacies in terms of probability laws on the unit interval and study the growth rate of maximal intricacies...

Measures of fuzziness and operations with fuzzy sets.

Siegfried Gottwald, Ernest Czogala, Witold Pedrycz (1982)

Stochastica

We discuss the effects that the usual set theoretic and arithmetic operations with fuzzy sets and fuzzy numbers have with respect to the energies and entropies of the fuzzy sets connected and of the resulting fuzzy sets, and we also compare the entropies and energies of the results of several of those operations.

Medidas de entropía en la teoría de la evidencia.

María Teresa Lamata Jiménez, Serafín Moral Callejón (1988)

Trabajos de Estadística

The aim of this paper is to define global measures of uncertainty in the framework of Dempster-Shafer's Theory of Evidence. Starting from the concepts of entropy and specificity introduced by Yager, two measures are considered; the lower entropy and the upper entropy.

Multi-variate correlation and mixtures of product measures

Tim Austin (2020)

Kybernetika

Total correlation (‘TC’) and dual total correlation (‘DTC’) are two classical ways to quantify the correlation among an n -tuple of random variables. They both reduce to mutual information when n = 2 . The first part of this paper sets up the theory of TC and DTC for general random variables, not necessarily finite-valued. This generality has not been exposed in the literature before. The second part considers the structural implications when a joint distribution μ has small TC or DTC. If TC ( μ ) = o ( n ) , then μ is...

Notion of information and independent component analysis

Una Radojičić, Klaus Nordhausen, Hannu Oja (2020)

Applications of Mathematics

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 analysis...

Currently displaying 121 – 140 of 268