Optimal Uncertainty Quantification

Understand

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront.

• This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information.
• In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information.
• Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions.