A Bayesian approach for the estimation of probability distributions under finite sample space

Abstract

In this article, we describe a Bayesian approach for the estimation of probability distribution of a discrete random variable (rv) with correlated classes under finite sample space. We utilize general benefits of Bayesian approaches within the context of estimation of probability distributions under finite sample space. In our approach, a tractable posterior distribution is obtained; and hence, posterior inferences are easily drawn by using the Gibbs sampling. Possible prior correlations between adjacent categories of the considered discrete rv are suitably modeled. The proposed approach takes into account all available information contained in successive samples as a natural consequence of using Bayes’s theorem. It is beneficial in the estimation of probability distributions for compositional data sets observed in longitudinal studies. We analyze two bar charts from two health surveys in Italy for illustrative purposes and apply our approach to a data set from general elections of Turkey.