  Despite numerous studies of deep autoencoders (AEs) for unsupervised anomaly
detection, AEs still lack a way to express uncertainty in their predictions,
crucial for ensuring safe and trustworthy machine learning systems in
high-stake applications. Therefore, in this work, the formulation of Bayesian
autoencoders (BAEs) is adopted to quantify the total anomaly uncertainty,
comprising epistemic and aleatoric uncertainties. To evaluate the quality of
uncertainty, we consider the task of classifying anomalies with the additional
option of rejecting predictions of high uncertainty. In addition, we use the
accuracy-rejection curve and propose the weighted average accuracy as a
performance metric. Our experiments demonstrate the effectiveness of the BAE
and total anomaly uncertainty on a set of benchmark datasets and two real
datasets for manufacturing: one for condition monitoring, the other for quality
inspection.
