Uncertainty Quantification of the 4th kind; optimal posterior accuracy-uncertainty tradeoff with the minimum enclosing ball

Understand

There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory.

• Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation.
• (B) requires a prior, it is generally brittle and posterior estimations can be slow.
• Although (C) leads to the identification of an optimal prior, its approximation suffers from the curse of dimensionality and the notion of risk is one that is averaged with respect to the distribution of the data.