The Uncertainty Analysis of Model Results: A Practical Guide

ISBN-13: 9783030094560 / Angielski / Miękka / 2019 / 346 str.

Eduard Hofer

Spis treści

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 of Uncertainties is Required

9.1 Introduction

9.2 Step 1: Search

9.3 Step 2: Quantify

9.4 Step 3: Propagate

9.4.1 Two nested Monte Carlo simulation loops

9.4.2 Low probability extreme value answers

9.5 Step 4: Estimate uncertainty

9.6 Step 5: Rank uncertainties

9.7 Step 6: Present the analysis and interpret its results

9.8 References

10 Practical Examples

10.1 Introduction

10.2 Uncertainty analysis of results from the application of a population

dynamics model

10.2.1 The assessment questions

10.2.2 The computer model

10.2.3 The analysis tool

10.2.4 The elicitation process

10.2.5 The potentially important uncertainties

10.2.6 Provisional state of knowledge quantifications

10.2.7 State of knowledge dependences

10.2.8 Model results obtained with best estimate parameter values

10.2.9 Propagation of the state of knowledge through the model

10.2.10 Uncertainty statements for selected model results

10.2.11 Uncertainty importance statements for selected model results

10.2.12 Conclusions

10.3 Uncertainty analysis of results from the application of a dose reconstruction

model

10.3.1 The assessment questions

10.3.2 The computer model

10.3.3 The analysis tool

10.3.4 The elicitation process

10.3.5 The potentially important uncertainties

10.3.6 The state of knowledge quantifications

10.3.7 State of knowledge dependences

10.3.8 Propagation of the state of knowledge through the model

10.3.9 Why two Monte Carlo simulation loops?

10.3.10 Answering the assessment questions

10.3.11 Uncertainty importance statements for selected model results

10.4 References

O autorze

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.

Blurb

This book is a practical guide to the uncertainty analysis of computer model applications. Used in many areas, such as engineering, ecology and economics, computer models are subject to various uncertainties at the level of model formulations, parameter values and input data. Naturally, it would be advantageous to know the combined effect of these uncertainties on the model results as well as whether the state of knowledge should be improved in order to reduce the uncertainty of the results most effectively. The book supports decision-makers, model developers and users in their argumentation for an uncertainty analysis and assists them in the interpretation of the analysis results.