The Uncertainty Analysis of Model Results (eBook)

Eduard Hofer holds a Master of Science diploma with distinction in mathematics from the Technical University of Munich (TUM), Germany. He developed a method for the numerical solution of initial value problems with large systems of stiff first-order ordinary differential equations. He also designed a non-commercial, PC-based software system for uncertainty analysis of results from computer models and conducted the uncertainty analysis of numerous applications of computationally demanding computer models. Hofer served on the external peer-review committee of a major US dose reconstruction study with the subtask in uncertainty and sensitivity analysis, and contributed to numerous international conferences. Furthermore, he received an award for his contributions in the field of probabilistic risk assessment.

Introduction and Necessary Distinctions1.1 The application of computer models1.2 Sources of epistemic uncertainty1.3 Verification and validation1.4 Why perform an analysis of epistemic uncertainty1.5 Source of aleatoric uncertainty1.6 Two different interpretations of ‘probability’1.7 Separation of uncertainties1.8 References2 Step 1: Search2.1 The scenario description2.2 The conceptual model2.3 The mathematical model2.4 The numerical model2.5 Conclusion3 Step 2: Quantify3.1 Subjective probability3.2 Data versus model uncertainty3.3 Ways to quantify data uncertainty3.3.1 Measurable quantities as uncertain data3.3.2 Functions of measurable quantities3.3.3 Distributions fitted to measurable quantities3.3.4 Sequences of uncertain input data3.3.5 Special cases3.4.1 Sets of alternative model formulations3.4.2 Two extreme models3.4.3 Corrections to the result from the preferred model3.4.4 Issues3.4.5 Some final remarks3.4.6 Completeness uncertainty3.5 Ways to quantify state of knowledge dependence3.5.1 How to identify state of knowledge dependence3.5.2 How to express state of knowledge dependence quantitatively3.5.3 Sample expressions of state of knowledge dependence3.5.4 A multivariate sample3.5.5 Summary of subchapter 3.53.6 State of knowledge elicitation and probabilistic modelling3.6.1 State of knowledge elicitation and probabilistic modelling for data3.6.2 State of knowledge elicitation and probabilistic modelling for modeluncertainties3.6.3 Elicitation for state of knowledge dependence3.7 Survey of expert judgment3.7.1 The structured formal survey of expert judgment3.7.2 The structured formal survey of expert judgment by questionnaire3.8 References4 Step 3: Propagate4.1 Introduction4.2 Random sampling4.3 Monte Carlo simulation4.4 Sampling methods4.4.1 Simple Random Sampling (SRS)4.4.2 Latin Hypercube Sampling (LHS)4.4.3 Importance sampling4.4.4 Subset sampling5 ReferencesStep 4: Estimate Uncertainty5.1 Uncertainty statements available from uncertainty propagation using simplerandom sampling (SRS)5.1.1 The meaning of confidence and confidence tolerance limits andintervals5.1.2 The mean value of the model result5.1.3 A quantile value of the model result5.1.4 A subjective probability interval for the model result5.1.5 Compliance of the model result with a limit value5.1.6 The sample variability of statistical tolerance limits5.1.7 Comparison of two model results5.1.8 Comparison of more than two model results5.2 Uncertainty statements available from uncertainty propagation using Latin5.2.1 Estimates of mean values of functions of the model result5.2.2 The mean value of the model result5.2.3 A quantile value5.2.4 A subjective probability interval5.2.5 Compliance with a limit value5.2.6 Comparison of two model results5.2.7 Comparison of more than two model results5.2.8 Estimates from replicated Latin Hypercube samples5.3 Graphical presentation of uncertainty analysis results5.3.1 Graphical presentation of uncertainty analysis results from SRS5.3.2 Graphical presentation of uncertainty analysis results from LHS5.4 References6 Step 5: Rank Uncertainties6.1 Introduction6.2 Differential sensitivity and “one-at-a-time” analysis6.3 Affordable measures for uncertainty importance ranking6.3.1 Uncertainty importance measures computed from raw data6.3.2 Uncertainty importance measures computed from ranktransformed data6.3.3 Practical examples6.4 Explaining the outliers6.5 Contributions to quality assurance6.6 Graphical presentation of uncertainty importance measures6.7 Conclusions6.8 References7 Step 6: Present the Analysis and Interpret its Results7.1 Presentation of the analysis7.2 Interpretation of the uncertainty estimate7.3 Interpretation of the importance ranking8 Practical Execution of the Analysis8.1 Support by analysis software8.2 Comparison of four software packages8.3 References9 Uncertainty Analysis when Separation of Uncertainties is Required9.1 Introduction9.2 Step 1: Search9.3 Step 2: Quantify9.4 Step 3: Propagate9.4.1 Two nested Monte Carlo simulation loops9.4.2 Low probability extreme value answers9.5 Step 4: Estimate uncertainty9.6 Step 5: Rank uncertainties9.7 Step 6: Present the analysis and interpret its results9.8 References10 Practical Examples10.1 Introduction10.2 Uncertainty analysis of results from the application of a populationdynamics model10.2.1 The assessment questions10.2.2 The computer model10.2.3 The analysis tool10.2.4 The elicitation process10.2.5 The potentially important uncertainties10.2.6 Provisional state of knowledge quantifications10.2.7 State of knowledge dependences10.2.8 Model results obtained with best estimate parameter values10.2.9 Propagation of the state of knowledge through the model10.2.10 Uncertainty statements for selected model results10.2.11 Uncertainty importance statements for selected model results10.2.12 Conclusions10.3 Uncertainty analysis of results from the application of a dose reconstructionmodel10.3.1 The assessment questions10.3.2 The computer model10.3.3 The analysis tool10.3.4 The elicitation process10.3.5 The potentially important uncertainties10.3.6 The state of knowledge quantifications10.3.7 State of knowledge dependences10.3.8 Propagation of the state of knowledge through the model10.3.9 Why two Monte Carlo simulation loops?10.3.10 Answering the assessment questions10.3.11 Uncertainty importance statements for selected model results10.4 References