  In healthcare applications, predictive uncertainty has been used to assess
predictive accuracy. In this paper, we demonstrate that predictive uncertainty
estimated by the current methods does not highly correlate with prediction
error by decomposing the latter into random and systematic errors, and showing
that the former is equivalent to the variance of the random error. In addition,
we observe that current methods unnecessarily compromise performance by
modifying the model and training loss to estimate the target and uncertainty
jointly. We show that estimating them separately without modifications improves
performance. Following this, we propose a novel method that estimates the
target labels and magnitude of the prediction error in two steps. We
demonstrate this method on a large-scale MRI reconstruction task, and achieve
significantly better results than the state-of-the-art uncertainty estimation
methods.
