  On top of machine learning models, uncertainty quantification (UQ) functions
as an essential layer of safety assurance that could lead to more principled
decision making by enabling sound risk assessment and management. The safety
and reliability improvement of ML models empowered by UQ has the potential to
significantly facilitate the broad adoption of ML solutions in high-stakes
decision settings, such as healthcare, manufacturing, and aviation, to name a
few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods
for ML models with a particular focus on neural networks and the applications
of these UQ methods in tackling engineering design as well as prognostics and
health management problems. Toward this goal, we start with a comprehensive
classification of uncertainty types, sources, and causes pertaining to UQ of ML
models. Next, we provide a tutorial-style description of several
state-of-the-art UQ methods: Gaussian process regression, Bayesian neural
network, neural network ensemble, and deterministic UQ methods focusing on
spectral-normalized neural Gaussian process. Established upon the mathematical
formulations, we subsequently examine the soundness of these UQ methods
quantitatively and qualitatively (by a toy regression example) to examine their
strengths and shortcomings from different dimensions. Then, we review
quantitative metrics commonly used to assess the quality of predictive
uncertainty in classification and regression problems. Afterward, we discuss
the increasingly important role of UQ of ML models in solving challenging
problems in engineering design and health prognostics. Two case studies with
source codes available on GitHub are used to demonstrate these UQ methods and
compare their performance in the life prediction of lithium-ion batteries at
the early stage and the remaining useful life prediction of turbofan engines.
