Bayesian nonparametric estimators derived from conditional Gibbs structures

Abstract

We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian nonparametric estimators, which can be readily exploited for predicting various features of additional samples. The results provide useful tools for genomic applications where prediction of future outcomes is required.Bayesian nonparametric inference; Exchangeable random partitions; Generalized factorial coeffcients; Generalized gamma process; Poisson-Dirichlet process; Population genetics.