Minimally informative nonparametric Bayesian procedures
Seminar Room 1, Newton Institute
We address the problem of how to conduct a minimally informative nonparametric Bayesian analysis. The central question is how to devise a model so that the posterior distribution satisfies a few basic properties. In order to satisfy these properties, the concept of local mass emerges, and the limiting Dirichlet process (or limdir) model is constructed. The notion of local mass suggests that nonparametric prior distributions be constructed in a different fashion than is typical. Use of the limdir model is illustrated for one-way analysis of variance with a pair of data sets. Consistency issues in this context are addressed.