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Global Sensitivity Analysis: The Primer

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Complex mathematical and computational models are used in all areas of society and technology and yet model based science is increasingly contested or refuted, especially when models are applied to controversial themes in domains such as health, the environment or the economy. More stringent standards of proofs are demanded from model-based numbers, especially when these numbers represent potential financial losses, threats to human health or the state of the environment. Quantitative sensitivity analysis is generally agreed to be one such standard.

Mathematical models are good at mapping assumptions into inferences. A modeller makes assumptions about laws pertaining to the system, about its status and a plethora of other, often arcane, system variables and internal model settings. To what extent can we rely on the model-based inference when most of these assumptions are fraught with uncertainties? Global Sensitivity Analysis offers an accessible treatment of such problems via  quantitative sensitivity analysis, beginning with the first principles and guiding the reader through the full range of recommended practices with a rich set of solved exercises. The text explains the motivation for sensitivity analysis, reviews the required statistical concepts, and provides a guide to potential applications.

The book:

  • Provides a self-contained treatment of the subject, allowing readers to learn and practice global sensitivity analysis without further materials.

  • Presents ways to frame the analysis, interpret its results, and avoid potential pitfalls.

  • Features numerous exercises and solved problems to help illustrate the applications.

  • Is authored by leading sensitivity analysis practitioners, combining a range of disciplinary backgrounds.

Postgraduate students and practitioners in a wide range of subjects, including statistics, mathematics, engineering, physics, chemistry, environmental sciences, biology, toxicology, actuarial sciences, and econometrics will find much of use here. This book will prove equally valuable to engineers working on risk analysis and to financial analysts concerned with pricing and hedging.

Author(s): A. Saltelli, Marco Ratto, Terry Andres, Francesca Campolongo, Jessica Cariboni, Debora Gatelli, Michaela Saisana, Stefano Tarantola
Publisher: Wiley-Interscience
Year: 2008

Language: English
Pages: 304

Global Sensitivity Analysis. The Primer......Page 3
Contents......Page 9
Preface......Page 13
1.1.1 Definition......Page 15
1.1.2 Models......Page 16
1.1.3 Models and Uncertainty......Page 17
1.1.4 How to Set Up Uncertainty and Sensitivity Analyses......Page 19
1.1.5 Implications for Model Quality......Page 23
1.2 Methods and Settings for Sensitivity Analysis – an Introduction......Page 24
1.2.1 Local versus Global......Page 25
1.2.2 A Test Model......Page 26
1.2.3 Scatterplots versus Derivatives......Page 27
1.2.4 Sigma-normalized Derivatives......Page 29
1.2.5 Monte Carlo and Linear Regression......Page 30
1.2.6 Conditional Variances – First Path......Page 34
1.2.7 Conditional Variances – Second Path......Page 35
1.2.8 Application to Model (1.3)......Page 36
1.2.9 A First Setting: ‘Factor Prioritization’......Page 38
1.2.10 Nonadditive Models......Page 39
1.2.11 Higher-order Sensitivity Indices......Page 43
1.2.12 Total Effects......Page 45
1.2.13 A Second Setting: ‘Factor Fixing’......Page 47
1.2.14 Rationale for Sensitivity Analysis......Page 48
1.2.15 Treating Sets......Page 50
1.2.16 Further Methods......Page 51
1.2.17 Elementary Effect Test......Page 52
1.2.18 Monte Carlo Filtering......Page 53
1.4 Possible Pitfalls for a Sensitivity Analysis......Page 55
1.5 Concluding Remarks......Page 56
1.7 Answers......Page 58
1.8 Additional Exercises......Page 64
1.9 Solutions to Additional Exercises......Page 65
2.1 Introduction......Page 67
2.2 Dependency on a Single Parameter......Page 69
2.3.1 Random Values......Page 72
2.3.2 Stratified Sampling......Page 73
2.3.3 Mean and Variance Estimates for Stratified Sampling......Page 75
2.4 Sensitivity Analysis of Multiple Parameters......Page 78
2.4.1 Linear Models......Page 79
2.4.2 One-at-a-time (OAT) Sampling......Page 80
2.4.3 Limits on the Number of Influential Parameters......Page 84
2.4.4 Fractional Factorial Sampling......Page 85
2.4.5 Latin Hypercube Sampling......Page 90
2.4.6 Multivariate Stratified Sampling......Page 94
2.4.7 Quasi-random Sampling with Low-discrepancy Sequences......Page 96
2.5 Group Sampling......Page 103
2.6 Exercises......Page 110
2.7 Exercise Solutions......Page 113
3.1 Introduction......Page 123
3.2 The Elementary Effects Method......Page 124
3.3 The Sampling Strategy and its Optimization......Page 126
3.4 The Computation of the Sensitivity Measures......Page 130
3.5 Working with Groups......Page 135
3.6 The EE Method Step by Step......Page 137
3.7 Conclusions......Page 141
3.8 Exercises......Page 142
3.9 Solutions......Page 145
4.1 Different Tests for Different Settings......Page 169
4.2 Why Variance?......Page 171
4.3 Variance-based Methods. A Brief History......Page 173
4.4 Interaction Effects......Page 175
4.5 Total Effects......Page 176
4.6 How to Compute the Sensitivity Indices......Page 178
4.7 FAST and Random Balance Designs......Page 181
4.8 Putting the Method to Work: The Infection Dynamics Model......Page 183
4.10 Exercises......Page 188
5.1 Introduction......Page 197
5.2 Monte Carlo Filtering (MCF)......Page 198
5.2.1 Implementation of Monte Carlo Filtering......Page 199
5.2.2 Pros and Cons......Page 201
5.2.3 Exercises......Page 203
5.2.4 Solutions......Page 204
5.2.5 Examples......Page 214
5.3 Metamodelling and the High-Dimensional Model Representation......Page 226
5.3.1 Estimating HDMRs and Metamodels......Page 228
5.3.2 A Simple Example......Page 238
5.3.3 Another Simple Example......Page 241
5.3.4 Exercises......Page 243
5.3.5 Solutions to Exercises......Page 245
5.4 Conclusions......Page 249
6 Sensitivity Analysis: From Theory to Practice......Page 251
6.1.1 Setting the Problem......Page 252
6.1.2 A Composite Indicator Measuring Countries’ Performance in Environmental Sustainability......Page 253
6.1.3 Selecting the Sensitivity Analysis Method......Page 255
6.1.4 The Sensitivity Analysis Experiment and Results......Page 256
6.1.5 Conclusions......Page 266
6.2.1 Setting the Problem......Page 267
6.2.2 The Heston Stochastic Volatility Model with Jumps......Page 269
6.2.4 The Sensitivity Analysis Experiment and Results......Page 272
6.2.5 Conclusions......Page 275
6.3.1 Setting the Problem......Page 276
6.3.2 Thermal Runaway Analysis of a Batch Reactor......Page 277
6.3.4 The Sensitivity Analysis Experiment and Results......Page 280
6.3.5 Conclusions......Page 283
6.4.1 In Brief......Page 284
6.5 When to use What?......Page 286
Afterword......Page 291
Bibliography......Page 293
Index......Page 301