Clustering structure for species sampling sequences with general base measure

Abstract

We investigate the clustering structure of species sampling sequences $(\xi_n)_n$, with general base measure. Such sequences are exchangeable with a species sampling random probability as directing measure. The clustering properties of these sequences are interesting for Bayesian nonparametrics applications, where mixed base measures are used, for example, to accommodate sharp hypotheses in regression problems and provide sparsity. In this paper, we prove a stochastic representation for $(\xi_n)_n$ in terms of a latent exchangeable random partition. We provide explicit expression of the EPPF of the partition generated by $(\xi_n)_n$ in terms of the EPPF of the latent partition. We investigate the asymptotic behaviour of the total number of blocks and of the number of blocks with fixed cardinality in the partition generated by $(\xi_n)_n$.