Moment Conditions and Bayesian Non-Parametrics

Abstract

Summary 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.

Inference Based on Structural Vector Autoregressions Identified With Sign and Zero Restrictions: Theory and Applications

“…11 For instance, this measure was used in Bornn, Shephard, and Solgi (2016). 12 A family of distributions is conjugate if the prior distribution being a member of this family implies that the posterior distribution is a member of the family.…”

Bayesian Estimation and Comparison of Moment Condition Models

“…On the theory side, Yang and He (2012) shows the asymptotic normality of the Bayesian EL posterior distribution of the quantile regression parameter, and Fang and Mukerjee (2006) and Chang and Mukerjee (2008) study the higher-order asymptotic and coverage properties of the Bayesian EL/ETEL posterior distribution for the population mean, while Schennach (2005) and Lancaster and Jun (2010) consider the large-sample behavior of the Bayesian ETEL posterior distribution under the assumption that all moment restrictions are valid. Alternative, non-EL/ETEL based approaches for moment condition models, which we do not consider in this paper, have also been examined, for example, Bornn et al (2015), Florens and Simoni (2016) and Kitamura and Otsu (2011).…”

Complementary Bayesian method of moments strategies

“…Here we shall presume that the joint prior has the form p ( ρ , θ )= p ( ρ ) p o ( θ ). Relevant statistical methods—Bornn et al (), Shin (), Gallant et al (), Schennach (), and Gallant () —were discussed earlier.…”

“…A Bayesian Group (1) approach is a difficult to implement when the moment equations are overidentified because the support of the posterior has Lebesgue measure zero. See Bornn et al () for a discussion of the issues, a review of the literature, and proposed remedies for likelihoods with discrete support using notions from geometric measure theory. For just identified moment equations the problem simplifies (Chamberlain & Imbens, ).…”