  Bayesian inference can quantify uncertainty in the predictions of neural
networks using posterior distributions for model parameters and network output.
By looking at these posterior distributions, one can separate the origin of
uncertainty into aleatoric and epistemic contributions. One goal of uncertainty
quantification is to inform on prediction accuracy. Here we show that
prediction accuracy depends on both epistemic and aleatoric uncertainty in an
intricate fashion that cannot be understood in terms of marginalized
uncertainty distributions alone. How the accuracy relates to epistemic and
aleatoric uncertainties depends not only on the model architecture, but also on
the properties of the dataset. We discuss the significance of these results for
active learning and introduce a novel acquisition function that outperforms
common uncertainty-based methods. To arrive at our results, we approximated the
posteriors using deep ensembles, for fully-connected, convolutional and
attention-based neural networks.
