A Modified Generalized Likelihood Uncertainty Estimation (GLUE) Methodology: Considering the Subjectivity of Likelihood Function Selection

The Generalized Likelihood Uncertainty Estimation (GLUE) methodology has been widely used in many areas as an effective and general strategy for model calibration and uncertainty estimation associated with complex models. A formal definition of a likelihood function (measure) is needed in the GLUE methodology. However, it has been recognized that the choice of a likelihood measure is inherently subjective, which, in turn, introduces a new kind of uncertainty-the epistemic uncertainty in the GLUE methodology. In this study, we developed a practical framework to address this uncertainty. To apply the GLUE methodology, we propose that multiple likelihood functions be used and results combined based on probability theory. Through an analysis of the probabilities of four infiltration maps at Yucca Mountain, Nevada, we demonstrate (1) it is important to consider the uncertainty caused by the subjectivity of the likelihood selection in the GLUE application; and (2) the proposed method can effectively address this epistemic uncertainty.