  This paper studies quasi Bayesian estimation and uncertainty quantification
for an unknown function that is identified by a nonparametric conditional
moment restriction. We derive contraction rates for a class of Gaussian process
priors. Furthermore, we provide conditions under which a Bernstein von Mises
theorem holds for the quasi-posterior distribution. As a consequence, we show
that optimally weighted quasi-Bayes credible sets have exact asymptotic
frequentist coverage.
