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

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.

Uncertainty analysis of the global hydrological model WGHM using the GLUE method for multi-type variables in the Mississippi basin

<p>In this research we evaluated the WaterGAP Global Hydrological Model (WGHM) parameter uncertainties and predictive intervals for multi-type variables, including streamflow, total water storage anomaly (TWSA) and snow cover based on the Generalized Likelihood Uncertainty Estimation (GLUE) method, for a large river basin in North America, the Mississippi basin. The GLUE approach is built on Monte Carlo concept, in which simulations are performed for all the parameter sets. The parameter sets are sampled from a prior range of the parameters using the Latin Hypercube Sampling. The Nash-Sutcliffe efficiency was used as likelihood measure in case of all variables. The behavioral set of models were selected as those which result likelihood measures above the pre-specified thresholds for all three variables or subsets. These behavioral parameters set were used to analyze different parameters uncertainties, trade-offs among the variables, and the influence of each individual observation data on constraining other variables.</p>

Anomaly Detection and Accuracy Measurement for Categorical Data

The Department of Defense (DoD) recently initiated an effort to compile all inter-service maintenance data for equipment and infrastructure, requiring the consolidation of maintenance records from over 40 different data sources. This research evaluates and improves the accuracy of this maintenance data warehouse by means of value modeling and statistical methods for anomaly detection. The first step in this work included the categorization of error-identifying metadata, which was then consolidated into a weighted scoring model. The most novel aspect of the work involved error identification processes using conditional probability combinations and likelihood measures. This analysis showed promising results, successfully identifying numerous invalid maintenance description labels through the use of conditional probability tests. This process has potential to both reduce the amount of manual labor necessary to clean the DoD maintenance data records and provide better fidelity on DoD maintenance activities.

Evaluation of Four GLUE Likelihood Measures and Behavior of Large Parameter Samples in ISPSO-GLUE for TOPMODEL

We tested four likelihood measures including two limits of acceptability and two absolute model residual methods within the generalized likelihood uncertainty estimation (GLUE) framework using the topography model (TOPMODEL). All these methods take the worst performance of all time steps as the likelihood of a model and none of these methods were successful in finding any behavioral models. We believe that reporting this failure is important because it shifted our attention from which likelihood measure to choose to why these four methods failed and how to improve these methods. We also observed how large parameter samples impact the performance of a hybrid uncertainty estimation method, isolated-speciation-based particle swarm optimization (ISPSO)-GLUE using the Nash–Sutcliffe (NS) coefficient. Unlike GLUE with random sampling, ISPSO-GLUE provides traditional calibrated parameters as well as uncertainty analysis, so over-conditioning the model parameters on the calibration data can affect its uncertainty analysis results. ISPSO-GLUE showed similar performance to GLUE with a lot less model runs, but its uncertainty bounds enclosed less observed flows. However, both methods failed in validation. These findings suggest that ISPSO-GLUE can be affected by over-calibration after a long evolution of samples and imply that there is a need for a likelihood measure that can better explain uncertainties from different sources without making statistical assumptions.

Parameter Estimation and Uncertainty Analysis of ORYZA_V3 Model Using the GLUE Method

The Generalized Likelihood Uncertainty Estimation (GLUE) method is one of the popular methods for parameter estimation and uncertainty analysis, although it has been criticized for some drawbacks in numerous studies. In this study, we performed an uncertainty analysis for the ORYZA_V3 model using the GLUE method integrated with Latin hypercube sampling (LHS). Different likelihood measures were examined to understand the differences in derived posterior parameter distributions and uncertainty estimates of the model predictions based on a variety of observations from field experiments. The results indicated that the parameter posterior distributions and 95% confidence intervals (95CI) of model outputs were very sensitive to the choice of likelihood measure, as well as the weights assigned to observations at different dates and to different observation types within a likelihood measure. Performance of the likelihood measure with a proper likelihood function based on normal distribution of model errors and the combining method based on mathematical multiplication was the best, with respect to the effectiveness of reducing the uncertainties of parameter values and model predictions. Moreover, only the means and standard deviations of observation replicates were enough to construct an effective likelihood function in the GLUE method. This study highlighted the importance of using appropriate likelihood measures integrated with multiple observation types in the GLUE method. Keywords: GLUE, Likelihood measures, Model uncertainty, Crop model.