A special Dirichlet mixture model in a Bayesian perspective

This contribution presents two Bayesian procedures - both based on Gibbs sampling - in order to estimate the parameters of the Flexible Dirichlet (Ongaro & Migliorati, 2013), a distribution for compositional data (i.e. data whose support is the simplex). This distribution can fit data better than the classical Dirichlet distribution, thanks to its mixture structure and additional parameters that allow for a more flexible modeling of the covariance matrix. A simulation study has been conducted in order to evaluate the performances of the proposed estimation algorithms in several parameters configuration. Data are generated from a Flexible Beta, the univariate version of the Flexible Dirichlet distribution.