Tsallis and other generalised entropy forms subject to Dirichlet mixture priors
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Date
Authors
Ferreira, Johannes Theodorus
Botha, Tanita
Bekker, Andriette, 1958-
Journal Title
Journal ISSN
Volume Title
Publisher
MDPI
Abstract
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.
Description
DATA AVAILABILITY STATEMENT: The data under consideration in this study is in the public domain
Keywords
Flexible Dirichlet, Functional, Moments, Posterior, Wasserstein
Sustainable Development Goals
Citation
Ferreira, 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.