1. Introduction
1.1. Overview of International Benchmarks Related to BEPU and UQ
1.2. Overview of Available IUQ Methods for System TH Codes
1.3. IUQ vs. Calibration
2. Definition of the IUQ Problem
3. The Full and Modular Bayesian Approaches
3.1. Fundamentals of Bayesian Inference
3.2. Bayesian IUQ
3.3. Full vs. Modular Bayesian Approaches for Bayesian IUQ
3.4. Applications and Variations of MBA
3.5. Applications and Variations of General Bayesian IUQ
4. IUQ Methods Developed/Used in the PREMIUM Benchmark
4.1. The CIRCÉ Method Developed by CEA
4.2. The IPREM Method Developed by UNIPI
4.3. CET-based Sample Adjusting Approach Developed by GRS
4.4. DIPE Developed by IRSN
4.5. MCDA Developed by KAERI
4.6. Bayesian Inference Method Used by PSI
4.7. Sampling-based IUQ Developed by Tractebel
4.8. Other Work Relevant to the PREMIUM Benchmark
5. The SAPIUM Project
6. Other IUQ Approaches
6.1. Bayesian and Non-linear Extensions of CIRCÉ by CEA Saclay
6.2. Non-parametric Clustering by PSI
6.3. Data Adjustment and Assimilation by KIT
6.4. CASUALIDAD by NINE
6.5. MLE and MAP by UIUC
6.6. Other IUQ Methods
6.7. IUQ in Other Nuclear M&S Areas
7. Evaluation of the Reviewed IUQ Methods
8. Challenges and Research Needs
8.1. Mathematical Description of the Model Bias Term in Bayesian IUQ
8.2. Confounding and Non-identifiability in IUQ
8.3. Extrapolation of the Model Bias
8.4. Incorporation of Uncertainties from Design Variables
8.5. More Open Issues for Future Development
9. Conclusions
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