  We consider the problem of aggregating predictions or measurements from a set
of human forecasters, models, sensors or other instruments which may be subject
to bias or miscalibration and random heteroscedastic noise. We propose a
Bayesian consensus estimator that adjusts for miscalibration and noise and show
that this estimator is unbiased and asymptotically more efficient than naive
alternatives. We further propose a Hierarchical Bayesian Model that leverages
our proposed estimator and apply it to two real world forecasting challenges
that require consensus estimates from error prone individual estimates:
forecasting influenza like illness (ILI) weekly percentages and forecasting
annual earnings of public companies. We demonstrate that our approach is
effective at mitigating bias and error and results in more accurate forecasts
than existing consensus models.
