ABSTRACT

We review the use of Bayesian nonparametric priors for inference in mixtures. Interpreting a mixture model as an expectation with respect to a mixing measure, it becomes natural to complete the model with a prior probability model on the unknown mixing measure. Prior models on random probability measures, like the mixing measure here, are known as Bayesian nonparametric models. We review some commonly used models, including in particular the Dirichlet process prior, normalized random measures with independent increments, and the determinantal point process and variations. Many applications of such models include inference on the implied partition of the experimental units, that is, a clustering of the data. This gives rise to predictive distributions that again take the form of a mixture model.