Understanding the Impacts Induced by Cut-Off Thresholds and Likelihood Measures on Confidence Interval When Applying GLUE Approach

Abstract Generalized likelihood uncertainty estimate (GLUE) approach are heavily affected by the choices of cut-off thresholds and likelihood measures. This work attempts to study the potential mechanisms behind the impacts induced by cut-off thresholds and likelihood measures on confidence interval obtained by GLUE. A theoretical analysis on typical likelihood measures reveals that the error model of likelihood measure has essential impacts on the sampling processes of GLUE. Likelihood measures based on a same error model are mathematically transferrable, leading to an identical population of acceptable parameter sets. A case study is conducted by applying GLUE to uncertainty analysis on daily flows simulated by HBV model for the source region of the Yellow River basin. Seven interval indicators are adopted to describe the geometric features of confidence intervals, which are integrated into a comprehensive score for an overall assessment by multiple attribute decision making (MADM) framework. Results indicate that 1) With an increase of cut-off threshold, confidence interval widens in low-level flow sections, moves upward in recession phases of medium-level flow sections whereas narrows in high-level flow sections. Trade-off mechanism amongst widening, moving and narrowing trends is a potential reason behind the variations of interval indicators with cut-off threshold. 2) Much higher similarities in confidence intervals can be detected for likelihood measures based on a same error model than those based on different error models; 3) increasing cut-off threshold highlights the impacts induced by the error models of likelihood measures, whereas weakens the impacts induced by the formulas of likelihood measures.