We propose a nonparametric Bayesian approach for conducting inference on probabilistic surveys. We use this approach to study whether US Survey of Professional Forecasters density projections for output growth and inflation are consistent with the noisy rational expectations hypothesis. We find that in contrast to theory for horizons close to two years there is no relationship whatsoever between subjective uncertainty and forecast accuracy for output growth density projections, both across forecasters and over time, and only a mild relationship for inflation projections. As the horizons shortens, the relationship becomes one-to-one, as the theory would predict.