Moment conditions and Bayesian nonparametrics

TL;DR

This paper introduces a Bayesian nonparametric framework for models defined by moment conditions, addressing the challenges of posterior support on manifolds with new probability and computational tools.

Contribution

It develops novel methods using Hausdorff measures for Bayesian analysis of models with moment conditions, applicable to various complex statistical models.

Findings

Successfully analyzed models on real and simulated data

Extended Bayesian methods to quasi-likelihoods and hierarchical models

Provided computational tools for manifold-supported posteriors

Abstract

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.