Accurate measurements of probabilistic beliefs have become increasingly important both in practice and in academia. Introduced by statisticians in the 1950s to promote truthful reports in simple environments, Proper Scoring Rules (PSR) are now arguably the most popular incentivized mechanisms to...

This paper proposes a new Bayesian approach for estimating, nonparametrically, parameters in econometric models that are characterized as the solution of a linear inverse problem. By using a Gaussian process prior distribution we propose the posterior mean as an estimator and prove consistency,...

The focus of the paper is the nonparametric estimation of an instrumental regression function ϕ defined by conditional moment restrictions stemming from a structural econometric model: E [Y − ϕ (Z) | W] = 0, and involving endogenous variables Y and Z and instruments W . The function ϕ is...