Estimating normal means with a conjugate style dirichlet process prior

Abstract

The problem of estimating many normal means is approached by means of an hierarchical model. The hierarchical model is the standard conjugate model with one exception: the normal distribution at the middle stage is replaced by a Dirichlet process with a normal shape. Estimation for this model is accomplished through the implementation of the Gibbs sampler (see Escobar and West,1991)Thisarticle describes a new Gibbs sampler algorithm that is implemented on a collapsed state space Results that apply to a general setting are obtained, suggesting that a collapse of the state space willimprove the rate of convergence of the Gibbs sampler. An example shows that the proposed collapse of the state space may result in a dramatically improved algorithm