The Bayesian information criterion (BIC) is one of the most popular criteria for model selection in finite mixture models. However, it implausibly penalizes the complexity of each component using the whole sample size and completely ignores the clustered structure inherent in the data, resulting...

Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Indeed, many popular nonparametric priors, such as the Dirichlet and the Pitman–Yor process priors, select...