# Uncertainty Analysis with High Dimensional Dependence Modelling. Wiley Series in Probability and Statistics

• ID: 2180872
• Book
• 302 Pages
• John Wiley and Sons Ltd
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Mathematical models are used to simulate complex real–world phenomena in many areas of science and technology. Large complex models typically require inputs whose values are not known with certainty. Uncertainty analysis aims to quantify the overall uncertainty within a model, in order to support problem owners in model–based decision–making. In recent years there has been an explosion of interest in uncertainty analysis. Uncertainty and dependence elicitation, dependence modelling, model inference, efficient sampling, screening and sensitivity analysis, and probabilistic inversion are among the active research areas. This text provides both the mathematical foundations and practical applications in this rapidly expanding area, including:
•  An up–to–date, comprehensive overview of the foundations and applications of uncertainty analysis.
• All the key topics, including uncertainty elicitation, dependence modelling, sensitivity analysis and probabilistic inversion.
• Numerous worked examples and applications.
• Workbook problems, enabling use for teaching.
• Software support for the examples, using UNICORN a Windows–based uncertainty modelling package developed by the authors.
• A website featuring a version of the UNICORN software tailored specifically for the book, as well as computer programs and data sets to support the examples.

Uncertainty Analysis with High Dimensional Dependence Modelling offers a comprehensive exploration of a new emerging field. It will prove an invaluable text for researches, practitioners and graduate students in areas ranging from statistics and engineering to reliability and environmetrics.

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Preface ix

1 Introduction 1

1.1 Wags and Bogsats 1

1.2 Uncertainty analysis and decision support: a recent example 4

1.3 Outline of the book 9

2 Assessing Uncertainty on Model Input 13

2.1 Introduction 13

2.2 Structured expert judgment in outline 14

2.3 Assessing distributions of continuous univariate uncertain quantities 15

2.4 Assessing dependencies 16

2.5 Unicorn 20

2.6 Unicorn projects 20

3 Bivariate Dependence 25

3.1 Introduction 25

3.2 Measures of dependence 26

3.3 Partial, conditional and multiple correlations 32

3.4 Copulae 34

3.5 Bivariate normal distribution 50

3.6 Multivariate extensions 51

3.7 Conclusions 54

3.8 Unicorn projects 55

3.9 Exercises 61

3.10 Supplement 67

4 High–dimensional Dependence Modelling 81

4.1 Introduction 81

4.2 Joint normal transform 82

4.3 Dependence trees 86

4.4 Dependence vines 92

4.5 Vines and positive definiteness 105

4.6 Conclusions 111

4.7 Unicorn projects 111

4.8 Exercises 115

4.9 Supplement 116

5 Other Graphical Models 131

5.1 Introduction 131

5.2 Bayesian belief nets 131

5.3 Independence graphs 141

5.4 Model inference 142

5.5 Conclusions 150

5.6 Unicorn projects 150

5.7 Supplement 157

6 Sampling Methods 159

6.1 Introduction 159

6.2 (Pseudo–) random sampling 160

6.3 Reduced variance sampling 161

6.4 Sampling trees, vines and continuous bbn s 168

6.5 Conclusions 180

6.6 Unicorn projects 180

6.7 Exercise 184

7 Visualization 185

7.1 Introduction 185

7.2 A simple problem 186

7.5 Scatter plots, matrix and overlay scatter plots 188

7.6 Cobweb plots 191

7.7 Cobweb plots local sensitivity: dike ring reliability 195

7.8 Radar plots for importance; internal dosimetry 199

7.9 Conclusions 201

7.10 Unicorn projects 201

7.11 Exercises 203

8 Probabilistic Sensitivity Measures 205

8.1 Introduction 205

8.2 Screening techniques 205

8.3 Global sensitivity measures 214

8.4 Local sensitivity measures 222

8.5 Conclusions 227

8.6 Unicorn projects 228

8.7 Exercises 230

8.8 Supplement 236

9 Probabilistic Inversion 239

9.1 Introduction 239

9.2 Existing algorithms for probabilistic inversion 240

9.3 Iterative algorithms 243

9.4 Sample re–weighting 246

9.5 Applications 249

9.6 Convolution constraints with prescribed margins 253

9.7 Conclusions 255

9.8 Unicorn projects 256

9.9 Supplement 258

10 Uncertainty and the UN Compensation Commission 269

10.1 Introduction 269

10.2 Claims based on uncertainty 270

10.3 Who pays for uncertainty 272

Bibliography 273

Index 281

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