  Due to their increasing spread, confidence in neural network predictions
became more and more important. However, basic neural networks do not deliver
certainty estimates or suffer from over or under confidence. Many researchers
have been working on understanding and quantifying uncertainty in a neural
network's prediction. As a result, different types and sources of uncertainty
have been identified and a variety of approaches to measure and quantify
uncertainty in neural networks have been proposed. This work gives a
comprehensive overview of uncertainty estimation in neural networks, reviews
recent advances in the field, highlights current challenges, and identifies
potential research opportunities. It is intended to give anyone interested in
uncertainty estimation in neural networks a broad overview and introduction,
without presupposing prior knowledge in this field. A comprehensive
introduction to the most crucial sources of uncertainty is given and their
separation into reducible model uncertainty and not reducible data uncertainty
is presented. The modeling of these uncertainties based on deterministic neural
networks, Bayesian neural networks, ensemble of neural networks, and test-time
data augmentation approaches is introduced and different branches of these
fields as well as the latest developments are discussed. For a practical
application, we discuss different measures of uncertainty, approaches for the
calibration of neural networks and give an overview of existing baselines and
implementations. Different examples from the wide spectrum of challenges in
different fields give an idea of the needs and challenges regarding
uncertainties in practical applications. Additionally, the practical
limitations of current methods for mission- and safety-critical real world
applications are discussed and an outlook on the next steps towards a broader
usage of such methods is given.
