Generalized Dirichlet distribution in Bayesian analysis

Abstract

Generalized Dirichlet distribution has a more general covariance structure than Dirichlet distribution. This makes the generalized Dirichlet distribution to be more practical and useful. The concept of complete neutrality will be used to derive the general moment function for the generalized Dirichlet distribution, and then some properties of the generalized Dirichlet distribution will be established. Similar to the Dirichlet distribution, the generalized Dirichlet distribution will be shown to conjugate to multinominal sampling. Two experiments are designed for studying the differences between the Dirichlet and the generalized Dirichlet distributions in Bayesian analysis. A method for generating samples from a generalized Dirichlet in presented. When a prior distribution is either a Dirichlet or a generalized Dirichlet distribution, the way for constructing such a prior is discussed.