Moment conditions and Bayesian nonparametrics

Models phrased though moment conditions are central to much of modern inference. 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 which involve simulating on a manifold can be applied widely, including providing Bayesian analysis of quasi-likelihoods, linear and nonlinear regression, missing data and hierarchical models.