Some issues on nonparametric Bayesian modeling using species sampling models

We review some aspects of nonparametric Bayesian data analysis with discrete random probability measures. We focus on the class of species sampling models (SSM). We critically investigate the common use of the Dirichlet process (DP) prior as a default SSM choice. We discuss alternative prior specications from a theoretical, computational and data analysis perspective. We conclude with a recommendation to consider SSM priors beyond the special case of the DP prior and make specic recommendations on how dierent choices can be used to re ect prior information and how they impact the desired inference. We show the required changes in the posterior simulation schemes, and argue that the additional generality can be achieved without additional computational eort.