  Neural networks have revolutionized the field of machine learning with
increased predictive capability. In addition to improving the predictions of
neural networks, there is a simultaneous demand for reliable uncertainty
quantification on estimates made by machine learning methods such as neural
networks. Bayesian neural networks (BNNs) are an important type of neural
network with built-in capability for quantifying uncertainty. This paper
discusses aleatoric and epistemic uncertainty in BNNs and how they can be
calculated. With an example dataset of images where the goal is to identify the
amplitude of an event in the image, it is shown that epistemic uncertainty
tends to be lower in images which are well-represented in the training dataset
and tends to be high in images which are not well-represented. An algorithm for
out-of-distribution (OoD) detection with BNN epistemic uncertainty is
introduced along with various experiments demonstrating factors influencing the
OoD detection capability in a BNN. The OoD detection capability with epistemic
uncertainty is shown to be comparable to the OoD detection in the discriminator
network of a generative adversarial network (GAN) with comparable network
architecture.
