Title: Structured Dirichlet mixtures as priors for generalised entropy estimation
Authors: Tanita Botha - University of Pretoria (South Africa) [presenting]
Johan Ferreira - University of Pretoria (South Africa)
Andriette Bekker - University of Pretoria (South Africa)
Abstract: Entropy indicates an amount of information contained in a system, and the suitable estimation of entropy continues to receive ongoing focus particularly in the case of multivariate data. Data on the unit simplex are often found in different spheres in science; particularly arising from compositional data. In these instances, the Dirichlet distribution is frequently employed as model of choice as prior in a Bayesian approach, but theoretically only accounts for possibilities of negatively correlated proportions. The purpose is to implement previously unconsidered mixtures of the Dirichlet distribution as a prior for the multinomial model that hypothetically allows for positive correlated data. Some statistical properties are briefly derived and the derived and fitted posterior model is used to obtain insight into the behaviour of some entropy forms for potential prior selection using real data, and a prior selection method is implemented to suggest a suitable prior for the consideration of the practitioner.