Optimal Uncertainty Quantification: Distributional Robustness Versus Bayesian Brittleness

We discuss recent mathematical and computational results on uncertainty quantification (UQ) in the presence of uncertainty about the correct probabilistic and physical models. Such UQ problems can be formulated as constrained optimization problems with information acting as the constraints, with consequent optimal assessments of risk, and advantages for interdisciplinary communication and open science. We also report consequences of this point of view for the robustness of Bayesian methods under prior perturbation.