Bayesian nonparametric analysis for a species sampling model with finitely many types

We derive explicit Bayesian nonparametric analysis for a species sampling model with finitely many types of Gibbs form of type $\alpha= -1$ recently introduced in Gnedin (2009). Our results complement existing analysis under Gibbs priors of type $\alpha \in [0, 1)$ proposed in Lijoi et al. (2008). Calculations rely on a groups sequential construction of Gibbs partitions introduced in Cerquetti (2008).