The Uncertainty Analysis of Model Results: A Practical Guide

Introduction and Necessary Distinctions 1.1 The application of computer models 1.2 Sources of epistemic uncertainty 1.3 Verification and validation 1.4 Why perform an analysis of epistemic uncertainty 1.5 Source of aleatoric uncertainty 1.6 Two different interpretations of 'probability' 1.7 Separation of uncertainties 1.8 References 2 Step 1: Search 2.1 The scenario description 2.2 The conceptual model 2.3 The mathematical model 2.4 The numerical model 2.5 Conclusion 3 Step 2: Quantify 3.1 Subjective probability 3.2 Data versus model uncertainty 3.3 Ways to quantify data uncertainty 3.3.1 Measurable quantities as uncertain data 3.3.2 Functions of measurable quantities
3.3.3 Distributions fitted to measurable quantities 3.3.4 Sequences of uncertain input data 3.3.5 Special cases 3.4.1 Sets of alternative model formulations
3.4.2 Two extreme models 3.4.3 Corrections to the result from the preferred model 3.4.4 Issues 3.4.5 Some final remarks 3.4.6 Completeness uncertainty 3.5 Ways to quantify state of knowledge dependence 3.5.1 How to identify state of knowledge dependence 3.5.2 How to express state of knowledge dependence quantitatively 3.5.3 Sample expressions of state of knowledge dependence
3.5.4 A multivariate sample 3.5.5 Summary of subchapter 3.5 3.6 State of knowledge elicitation and probabilistic modelling 3.6.1 State of knowledge elicitation and probabilistic modelling for data 3.6.2 State of knowledge elicitation and probabilistic modelling for model
uncertainties 3.6.3 Elicitation for state of knowledge dependence 3.7 Survey of expert judgment 3.7.1 The structured formal survey of expert judgment 3.7.2 The structured formal survey of expert judgment by questionnaire 3.8 References 4 Step 3: Propagate 4.1 Introduction 4.2 Random sampling 4.3 Monte Carlo simulation 4.4 Sampling methods 4.4.1 Simple Random Sampling (SRS) 4.4.2 Latin Hypercube Sampling (LHS) 4.4.3 Importance sampling 4.4.4 Subset sampling
5 References
Step 4: Estimate Uncertainty 5.1 Uncertainty statements available from uncertainty propagation using simple random sampling (SRS) 5.1.1 The meaning of confidence and confidence tolerance limits and intervals 5.1.2 The mean value of the model result 5.1.3 A quantile value of the model result 5.1.4 A subjective probability interval for the model result 5.1.5 Compliance of the model result with a limit value 5.1.6 The sample variability of statistical tolerance limits 5.1.7 Comparison of two model results 5.1.8 Comparison of more than two model results 5.2 Uncertainty statements available from uncertainty propagation using Latin 5.2.1 Estimates of mean values of functions of the model result
5.2.2 The mean value of the model result 5.2.3 A quantile value 5.2.4 A subjective probability interval 5.2.5 Compliance with a limit value 5.2.6 Comparison of two model results 5.2.7 Comparison of more than two model results 5.2.8 Estimates from replicated Latin Hypercube samples 5.3 Graphical presentation of uncertainty analysis results 5.3.1 Graphical presentation of uncertainty analysis results from SRS 5.3.2 Graphical presentation of uncertainty analysis results from LHS
5.4 References 6 Step 5: Rank Uncertainties 6.1 Introduction 6.2 Differential sensitivity and "one-at-a-time" analysis 6.3 Affordable measures for uncertainty importance ranking 6.3.1 Uncertainty importance measures computed from raw data 6.3.2 Uncertainty importance measures computed from rank
transformed data 6.3.3 Practical examples 6.4 Explaining the outliers 6.5 Contributions to quality assurance 6.6 Graphical presentation of uncertainty importance measures 6.7 Conclusions 6.8 References 7 Step 6: Present the Analysis and Interpret its Results 7.1 Presentation of the analysis 7.2 Interpretation of the uncertainty estimate 7.3 Interpretation of the importance ranking 8 Practical Execution of the Analysis 8.1 Support by analysis software 8.2 Comparison of four software packages 8.3 References 9 Uncertainty Analysis when Separation