The prior distribution is an essential ingredient of any Bayesian analysis, and it plays a major role in determining the final results. As such, Bayesians attempt to use prior distributions that have certain properties. Perhaps the main property is a desire to accurately reflect prior information, i.e., information external to the experiment at hand. We would supplement this vague property with a second equally vague property. The posterior distribution should exhibit behavior that is qualitatively acceptable. Nonparametric Bayesian methods provide a means of creating prior distributions that accurately reflect prior knowledge in the sense that they satisfy the basic desireable qualitative features of inference. In this work, we provide a framework that encompasses a wide range of nonparametric Bayesian models. The framework naturally suggests new classes of these models which are amenable to simulation based fits with the same technology used to fit finite mixture models and models based on Dirichlet process priors. This talk and a companion talk, which described spatial applications of these models, were presented at the 2001 JSM.

Key Words: Consistency, Dependent Dirichlet Process, Dirichlet Process, Logistic Regression, Overdisperstion, Point Referenced Spatial Data

The manuscript is available in postscript and pdf formats.