Moment conditions and Bayesian non‐parametrics

Models phrased through moment conditions are central to much of modern inference. Here these moment conditions are embedded within a non‐parametric Bayesian set‐up. 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 by using Hausdorff measures to analyse 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 non‐linear regression, missing data and hierarchical models.