  We study a methodology to tackle the NASA Langley Uncertainty Quantification
Challenge, a model calibration problem under both aleatory and epistemic
uncertainties. Our methodology is based on an integration of robust
optimization, more specifically a recent line of research known as
distributionally robust optimization, and importance sampling in Monte Carlo
simulation. The main computation machinery in this integrated methodology
amounts to solving sampled linear programs. We present theoretical statistical
guarantees of our approach via connections to nonparametric hypothesis testing,
and numerical performances including parameter calibration and downstream
decision and risk evaluation tasks.
