Bayesian Nonparametric and Parametric Inference

This paper reviews Bayesian Nonparametric methods and discusses how parametric predictive densities can be constructed using nonparametric ideas. 1 IntroductionI will start with what might seem an unfair comment, yet it is meant to be instructive. The topic I am writing about, “Bayesian nonparametric theory”, should, in my opinion, be entitled “Bayesian theory”. This name has however been reserved for “Bayesian parametric theory”. The goal of the Bayesian, in the first instance, is the constructionof a prior probability distribution on a space of density functions. Exactly how large a set of densities the prior covers is the first choice to be made; the second is the shape of the prior. It is fair to say that the larger the set of densities, the harder it is to put a probability on