The Flexible Dirichlet (Ongaro and Migliorati, J. Multivar. Anal. 114:412–426, 2013) is a distribution for compositional data (i.e., data whose support is the simplex), which can fit data better than the classical Dirichlet distribution, thanks to its mixture structure and to additional parameters that allow for a more flexible modeling of the covariance matrix. This contribution presents two Bayesian procedures—both based on Gibbs sampling—in order to estimate its parameters. A simulation study has been conducted in order to evaluate the performances of the proposed estimation algorithms in several parameter configurations. Data are generated from a Flexible Dirichlet with D = 3 components and with representative parameter configurations.
Ascari, R., Migliorati, S., Ongaro, A. (2019). Bayesian inference for a mixture model on the simplex. In D.L. Greselin F. (a cura di), Statistical Learning of Complex Data (pp. 103-110). Springer Berlin Heidelberg [10.1007/978-3-030-21140-0_11].
Bayesian inference for a mixture model on the simplex
Ascari, R;Migliorati, S;Ongaro, A
2019
Abstract
The Flexible Dirichlet (Ongaro and Migliorati, J. Multivar. Anal. 114:412–426, 2013) is a distribution for compositional data (i.e., data whose support is the simplex), which can fit data better than the classical Dirichlet distribution, thanks to its mixture structure and to additional parameters that allow for a more flexible modeling of the covariance matrix. This contribution presents two Bayesian procedures—both based on Gibbs sampling—in order to estimate its parameters. A simulation study has been conducted in order to evaluate the performances of the proposed estimation algorithms in several parameter configurations. Data are generated from a Flexible Dirichlet with D = 3 components and with representative parameter configurations.
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