Minimally informative prior distributions for non-parametric Bayesian analysis

We address the problem of how to conduct a minimally informative, non-parametric Bayesian analysis. The central question is how to devise a model so that the posterior distribution satisfies a few basic properties. The concept of 'local mass' provides the key to the development of the limiting Dirichlet process model. This model is then used to provide an engine for inference in the compound decision problem and for multiple-comparisons inference in a one-way analysis-of-variance setting. Our analysis in this setting may be viewed as a limit of the analyses that were developed by Escobar and by Gopalan and Berry. Computations for the analysis are described, and the predictive performance of the model is compared with that of mixture of Dirichlet processes models.