  Bayesian neural networks (BNNs) can account for both aleatoric and epistemic
uncertainty. However, in BNNs the priors are often specified over the weights
which rarely reflects true prior knowledge in large and complex neural network
architectures. We present a simple approach to incorporate prior knowledge in
BNNs based on external summary information about the predicted classification
probabilities for a given dataset. The available summary information is
incorporated as augmented data and modeled with a Dirichlet process, and we
derive the corresponding \emph{Summary Evidence Lower BOund}. The approach is
founded on Bayesian principles, and all hyperparameters have a proper
probabilistic interpretation. We show how the method can inform the model about
task difficulty and class imbalance. Extensive experiments show that, with
negligible computational overhead, our method parallels and in many cases
outperforms popular alternatives in accuracy, uncertainty calibration, and
robustness against corruptions with both balanced and imbalanced data.
