Bayesian nonparametric inference for shared species richness in multiple populations

We introduce the branching Ewens–Pitman sampling model for dependent species sequences. The model defines random probability measures having marginally two-parameter Poisson–Dirichlet process distributions. These random measures are associated with the nodes of a binary tree which describes the strength of dependence of the resulting random partitions. We discuss Bayesian analysis under the introduced model and provide algorithms for posterior inference. The model is applied to evaluate similarities across microbial populations in the human esophagus.