On species sampling sequences induced by residual allocation models

• We discuss fully Bayesian inference for a class of models induced by residual allocation priors.
• We give a generalization of the Ewens sampling formula for the class under study.
• We derive the exchangeable partition probability function for generalized Dirichlet and probit stick-breaking priors.
• A suitable computational strategy for fitting the models is described.

We discuss fully Bayesian inference in a class of species sampling models that are induced by residual allocation (sometimes called stick-breaking) priors on almost surely discrete random measures. This class provides a generalization of the well-known Ewens sampling formula that allows for additional flexibility while retaining computational tractability. In particular, the procedure is used to derive the exchangeable predictive probability functions associated with the generalized Dirichlet process of Hjort (2000) and the probit stick-breaking prior of Chung and Dunson (2009) and Rodriguez and Dunson (2011). The procedure is illustrated with applications to genetics and nonparametric mixture modeling.