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.
