Bayesian Non-parametrics

Abstract

This article discusses Bayesian nonparametric models, arguing that all Bayesians are constructing probability distributions (the prior) on spaces of density functions. The parametric Bayesian can be seen to be making restrictive assumptions about the choice of density for modelling data. In contrast, the nonparametric Bayesian constructs a probability distribution on as many densities as possible. The model is infinite dimensional, yet inference is possible, including density estimation and the implementation of decision rules, such as the maximization of expected utility. An example of a nonparametric model is given and a means by which to make inference provided by simulation techniques.