Dirichlet process ($\mathrm{DP}(\alpha ,G_0)$)

A Dirichlet process is a distribution over probability measures such that the masses assigned to every finite measurable partition have a Dirichlet distribution. Its draws are almost surely discrete.

A Dirichlet prior with parameters $({\alpha }_1,\dots ,{\alpha }_K)$ combined with categorical labels having counts $(N_1,\dots ,N_K)$ gives a Dirichlet posterior with parameters $({\alpha }_1+N_1,\dots ,{\alpha }_K+N_K)$.