Some Computational Aspects of a Noncentral Dirichlet Family

Botha, Tanita; Ferreira, Johan; Bekker, Andriëtte

doi:10.1007/978-3-031-13971-0_4

Cited by 1 publication

(1 citation statement)

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“…The Dirichlet distribution is well known when working with data on the unitary simplex (0, 1) and is a multivariate generalization of the beta distribution. Several generalizations of the Dirichlet distribution has been developed and investigated, such as a class of Dirichlet generators as explored in [4], the noncentral Dirichlet construction in [5], as well as the Dirichlet-gamma of [6] in order to strengthen the capability to model different dependence patterns.…”

Section: Introductionmentioning

confidence: 99%

Tsallis and Other Generalised Entropy Forms Subject to Dirichlet Mixture Priors

2022

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Entropy indicates a measure of information contained in a complex system, and its estimation continues to receive ongoing focus in the case of multivariate data, particularly that on the unit simplex. Oftentimes the Dirichlet distribution is employed as choice of prior in a Bayesian framework conjugate to the popular multinomial likelihood with K distinct classes, where consideration of Shannon- and Tsallis entropy is of interest for insight detection within the data on the simplex. However, this prior choice only accounts for negatively correlated data, therefore this paper incorporates previously unconsidered mixtures of Dirichlet distributions as potential priors for the multinomial likelihood which addresses the drawback of negative correlation. The power sum functional, as the product moment of the mixture of Dirichlet distributions, is of direct interest in the multivariate case to conveniently access the Tsallis- and other generalized entropies that is incorporated within an estimation perspective of the posterior distribution using real economic data. A prior selection method is implemented to suggest a suitable prior for the consideration of the practitioner; empowering the user in future for consideration of suitable priors incorporating entropy within the estimation environment as well as having the option of certain mixture of Dirichlet distributions that may require positive correlation.

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Section: Introductionmentioning

confidence: 99%