Approximate Bayesian Inference in Models Defined Through Estimating Equations

This chapter reviews recent approaches to Bayesian inference when the only information linking parameters and data is in the form of estimating equations. Bayesian inference in this class of models is difficult to implement since the likelihood function is left unspecified. The approaches reviewed in the chapter are those that rely on posterior constructed using frequentist objective functions, such as the Generalized Method of Moments and the Generalized Empirical Likelihood, as approximate likelihoods functions. We explore the Bayesian and frequentist properties of inference based on these posteriors.