Moment conditions and Bayesian nonparametrics

Models phrased though moment conditions are central to much of modern statistics and econometrics. Here these moment conditions are embedded within a nonparametric Bayesian setup. Handling such a model is not probabilistically straightforward as the posterior has support on a manifold. We solve the relevant issues, building new probability and computational tools using Hausdorff measures to analyze them on real and simulated data. These new methods can be applied widely, including providing Bayesian analysis of quasi-likelihoods, linear and nonlinear regression and quantile regression, missing data, set identified models, and hierarchical models.