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.
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.
1. Introduction to Sensitivity Analysi.
1.1 Models and Sensitivity Analysis.
1.1.3 Models and Uncertainty.
1.1.4 How to Set Up Uncertainty and Sensitivity Analyses.
1.1.5 Implications for Model Quality.
1.2 Methods and Settings for Sensitivity Analysis – An Introduction.
1.2.1 Local versus Global.
1.2.2 A Test Model.
1.2.3 Scatterplots versus Derivatives.
1.2.4 Sigma–normalized Derivatives.
1.2.5 Monte Carlo and Linear Regression.
1.2.6 Conditional Variances – First Path.
1.2.7 Conditional Variances – Second Path.
1.2.8 Application to Model (1.3).
1.2.9 A First Setting: ′Factor Prioritization′
1.2.10 Nonadditive Models.
1.2.11 Higher–order Sensitivity Indices.
1.2.12 Total Effects.
1.2.13 A Second Setting: ′Factor Fixing′.
1.2.14 Rationale for Sensitivity Analysis.
1.2.15 Treating Sets.
1.2.16 Further Methods.
1.2.17 Elementary Effect Test.
1.2.18 Monte Carlo Filtering.
1.3 Nonindependent Input Factors.
1.4 Possible Pitfalls for a Sensitivity Analysis.
1.5 Concluding Remarks.
1.8 Additional Exercises.
1.9 Solutions to Additional Exercises.
2. Experimental Designs.
2.2 Dependency on a Single Parameter.
2.3 Sensitivity Analysis of a Single Parameter.
2.3.1 Random Values.
2.3.2 Stratified Sampling.
2.3.3 Mean and Variance Estimates for Stratified Sampling.
2.4 Sensitivity Analysis of Multiple Parameters.
2.4.1 Linear Models.
2.4.2 One–at–a–time (OAT) Sampling.
2.4.3 Limits on the Number of Influential Parameters.
2.4.4 Fractional Factorial Sampling.
2.4.5 Latin Hypercube Sampling.
2.4.6 Multivariate Stratified Sampling.
2.4.7 Quasi–random Sampling with Low–discrepancy Sequences.
2.5 Group Sampling.
2.7 Exercise Solutions.
3. Elementary Effects Method.
3.2 The Elementary Effects Method.
3.3 The Sampling Strategy and its Optimization.
3.4 The Computation of the Sensitivity Measures.
3.5 Working with Groups.
3.6 The EE Method Step by Step.
4. Variance–based Methods.
4.1 Different Tests for Different Settings.
4.2 Why Variance?
4.3 Variance–based Methods. A Brief History.
4.4 Interaction Effects.
4.5 Total Effects.
4.6 How to Compute the Sensitivity Indices.
4.7 FAST and Random Balance Designs.
4.8 Putting the Method to Work: the Infection Dynamics Model.
5. Factor Mapping and Metamodelling.
5.2 Monte Carlo Filtering (MCF).
5.2.1 Implementation of Monte Carlo Filtering.
5.2.2 Pros and Cons.
5.3 Metamodelling and the High–Dimensional Model Representation.
5.3.1 Estimating HDMRs and Metamodels.
5.3.2 A Simple Example.
5.3.3 Another Simple Example.
5.3.5 Solutions to Exercises.
6. Sensitivity Analysis: from Theory to Practice.
6.1 Example 1: a Composite Indicator.
6.1.1 Setting the Problem.
6.1.2 A Composite Indicator Measuring Countries Performance in Environmental Sustainability.
6.1.3 Selecting the Sensitivity Analysis Method.
6.1.4 The Sensitivity Analysis Experiment and its Results.
6.2 Example 2: Importance of Jumps in Pricing Options.
6.2.1 Setting the Problem.
6.2.2 The Heston Stochastic Volatility Model with Jumps.
6.2.3 Selecting a Suitable Sensitivity Analysis Method.
6.2.4 The Sensitivity Analysis Experiment.
6.3 Example 3: a Chemical Reactor.
6.3.1 Setting the Problem.
6.3.2 Thermal Runaway Analysis of a Batch Reactor.
6.3.3 Selecting the Sensitivity Analysis Method.
6.3.4 The Sensitivity Analysis Experiment and its Results.
6.4 Example 4: a Mixed Uncertainty–Sensitivity Plot.
6.4.1 In Brief.
6.5 When to use What?