  We study a methodology to tackle the NASA Langley Uncertainty Quantification
Challenge problem, 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 boils down to solving
sampled linear programs. We will illustrate both our numerical performances and
theoretical statistical guarantees obtained via connections to nonparametric
hypothesis testing.
