Tsallis and other generalised entropy forms subject to Dirichlet mixture priors

dc.contributor.authorFerreira, Johannes Theodorus
dc.contributor.authorBotha, Tanita
dc.contributor.authorBekker, Andriette, 1958-
dc.contributor.emailtanita.botha@up.ac.zaen_US
dc.date.accessioned2023-03-06T07:09:43Z
dc.date.available2023-03-06T07:09:43Z
dc.date.issued2022-05-28
dc.descriptionDATA AVAILABILITY STATEMENT: The data under consideration in this study is in the public domainen_US
dc.description.abstractEntropy 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.en_US
dc.description.departmentStatisticsen_US
dc.description.librarianam2023en_US
dc.description.sponsorshipThe University of Pretoria; the DSTNRF South African Research Chair Initiative in Biostatistics; Statomet, University of Pretoria; as well as the Centre of Excellence in Mathematical and Statistical Sciences at the University of the Witwatersrand.en_US
dc.description.urihttps://www.mdpi.com/journal/symmetryen_US
dc.identifier.citationFerreira, J.T.; Botha, T.; Bekker, A. Tsallis and Other Generalised Entropy Forms Subject to Dirichlet Mixture Priors. Symmetry 2022, 14, 1110. https://DOI.org/10.3390/sym14061110.en_US
dc.identifier.issn2073-8994 (online)
dc.identifier.other10.3390/sym14061110
dc.identifier.urihttps://repository.up.ac.za/handle/2263/89968
dc.language.isoenen_US
dc.publisherMDPIen_US
dc.rights© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.en_US
dc.subjectFlexible Dirichleten_US
dc.subjectFunctionalen_US
dc.subjectMomentsen_US
dc.subjectPosterioren_US
dc.subjectWassersteinen_US
dc.titleTsallis and other generalised entropy forms subject to Dirichlet mixture priorsen_US
dc.typeArticleen_US

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