Bayesian estimation for a mixture of simplex distributions with an unknown number of components: HDI analysis in Brazil

Variables taking value in such as rates or proportions, are frequently analyzed by researchers, for instance, political and social data, as well as the Human Development Index (HDI). However, sometimes this type of data cannot be modeled adequately using a unique distribution. In this case, we can use a mixture of distributions, which is a powerful and flexible probabilistic tool. This manuscript deals with a mixture of simplex distributions to model proportional data. A fully Bayesian approach is proposed for inference which includes a reversible-jump Markov Chain Monte Carlo procedure. The usefulness of the proposed approach is confirmed by using of the simulated mixture data from several different scenarios and by using the methodology to analyze municipal HDI data of cities (or towns) in the Northeast region and SAo Paulo state in Brazil. The analysis shows that among the cities in the Northeast, some appear to have a similar HDI to other cities in SAo Paulo state.