Statistica Sinica 4(1994), 639-650

A CONSTRUCTIVE DEFINITION OF DIRICHLET PRIORS

Jayaram Sethuraman

Florida State University

Abstract: In this paper we give a simple and new constructive definition of Dirichlet measures removing the restriction that the basic space should be Rk. 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.