Bayesian Inference Using an Extension of the Dirichlet Process

Abstract

A family of nonparametric prior distributions which extends the Dirichlet process is introduced and studied. Such family is first constructed by normalising suitable compound Poisson processes. An alternative derivation shows that such priors admit a simple representation as discrete random probability measures with symmetric Dirichlet weights independent of i.i.d. locations. The latter representation proves useful in deriving manageable expressions for the posterior and predictive distributions. A number of Bayesian nonparametric estimators based on the family are discussed. Furthermore, an analysis of the characteristics of a sample drawn from the family demonstrates its potential as a second stage prior in hierarchical Bayesian clustering models.