Estimating normal means with a conjugate style Dirichlet process prior. (English) Zbl 0825.62053

Summary: 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). This article 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 will improve 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.


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