A comparative analysis of uncertainty quantification using the deviation-based cost function

Abstract

Uncertainty Quantification (UQ) is crucial in various domains. One of the main difficulties of UQ is the quantification of uncertainty sources. The present work compares three categories of methods for UQ using explicitly or implicitly related experimental data. They are (i) analytical method derived under the assumptions of Gaussian distribution and linear response, (ii) stochastic sampling method with selected weighting factors, and (iii) ab initio reference method based on the ${\chi }^2$ values measuring the differences between theoretical calculations and experimental data. The numerical studies show that even though the stochastic sampling method is generally better than the analytical one with specific weighting functions due to fewer assumptions, it differs from the reference results for all four weightings (including the present proposals) considered in the present study. Therefore, it is recommended to use the ab initio method unless the applicability of other explicit method(s) is justified.