Nonparametric Applications of Bayesian Inference

The paper evaluates the usefulness of a nonparametric approach to Bayesian inference by presenting two applications. The approach is due to Ferguson (1973, 1974) and Rubin (1981). Our first application considers an educational choice problem. We focus on obtaining a predictive distribution for earnings corresponding to various levels of schooling. This predictive distribution incorporates the parameter uncertainty, so that it is relevant for decision making under uncertainty in the expected utility framework of microeconomics. The second application is to quantile regression. Our point here is to examine the potential of the nonparametric framework to provide inferences without making asymptotic approximations. Unlike in the first application, the standard asymptotic normal approximation turns out to not be a good guide. We also consider a comparison with a bootstrap approach.