Editing Dirichlet distribution (section)

===Relation to Dirichlet-multinomial distribution===
In a model where a Dirichlet prior distribution is placed over a set of [[categorical distribution|categorical-valued]] observations, the [[marginal distribution|marginal]] [[joint distribution]] of the observations (i.e. the joint distribution of the observations, with the prior parameter [[marginalized out]]) is a [[Dirichlet-multinomial distribution]].  This distribution plays an important role in [[hierarchical Bayesian model]]s, because when doing [[statistical inference|inference]] over such models using methods such as [[Gibbs sampling]] or [[variational Bayes]], Dirichlet prior distributions are often marginalized out.  See the [[Dirichlet-multinomial distribution|article on this distribution]] for more details.