Statistica Sinica

Jayaram Sethuraman

Abstract:In this paper we give a simple and new constructive definition of Dirichlet measures removing the restriction that the basic space should beR_{k}. We also give complete, self contained proofs of the three basic results for Dirichlet measures:

1. The Dirichlet measure is a probability measure on the space of all probability measures.

2. It gives probability one to the subset of discrete probability measures.

3. The posterior distribution is also a Dirichlet measure.

Key words and phrases:Bayesian nonparametrics, random probability measures, Di- richlet measures.