  The goals of this chapter are twofold. First, we wish to introduce molecular
dynamics (MD) and uncertainty quantification (UQ) in a common setting in order
to demonstrate how the latter can increase confidence in the former. In some
cases, this discussion culminates in our providing practical, mathematical
tools that can be used to answer the question, "is this simulation reliable?"
However, many questions remain unanswered. Thus, a second goal of this work is
to highlight open problems where progress would aid the larger community.
