The distribution over distributions in the sense that each draw from the process is itself the distribution. The name Dirichlet process or procedure is due to the fact that the ?nite dimensional marginal distributions of the process follow Dirichlet distribution. Commonly used as a previous distribution in the nonparametric Bayesian models, mainly in Dirichlet process mixture models. This is called nonparametric because, though the distributions drawn from the Dirichlet process are discrete, they cannot be defined using the ?nite number of parameters. The prior distribution induced by the Dirichlet procedure can be obtained incrementally using the Chinese restaurant process.