Global Sensitivity Analysis. The Primer. Joint Research Centre uf the European Commission, Ispra,

Transcription

1 Global Sensitivity Analysis. The Primer Andrea Saltelli, Marco Ratto, Joint Research Centre ofthe European Commission, Ispra, Italy Terry Andres Department of Computer Science, University of Manitoba, Canada Francesca Campolongo, Jessica Cariboni, Debora Gatelli, Michaela Saisana and Stefano Tarantola Joint Research Centre uf the European Commission, Ispra, Italy ~John Wiley &. Sons, Ltd

2 Contents Preface Xl Introduction to Sensitivity Analysis. Models and Sensitivity Analysis.. Definition..2 Models..3 Models and Uncertainty..4 How to Set Up Uncertainty and Sensitivity Analyses..5 Implications for Model Quality.2 Methods and Settings for Sensitivity Analysis - an Introduction.2. Local versus Global.2.2 A Test Model.2.3 Scatterplots versus Derivatives.2.4 Sigma-normalized Derivatives.2.5 Monte Carlo and Linear Regression.2.6 Conditional Variances - First Path.2.7 Conditional Variances - Second Path.2.8 Application to Model (.3).2.9 A First Setting; 'Factor Prioritization'.2.0 Nonadditive Models.2. Higher-order Sensitivity Indices.2.2 Total Effects.2.3 A Second Setting: 'Factor Fixing'.2.4 Rationale for Sensitivity Analysis.2.5 Treating Sets.2.6 Further Methods.2.7 Elementary Effect Test.2.8 Monte Carlo Filtering.3 Nonindependent Input Factors.4 Possible Pitfalls for a Sensitivity Analysis.5 Concluding Remarks

3 VIII CONTENTS.6 Exercises 44.7 Answers 44.8 Additional Exercises 50.9 Solutions to Additional Exercises 5 2 Experimental Designs Introduction Dependency on a Single Parameter Sensitivity Analysis of a Single Parameter Random Values Stratified Sampling Mean and Variance Estimates for Stratified Sampling Sensitivity Analysis of Multiple Parameters Linear Models One-at-a-time (OAT) Sampling Limits on the Number of Influential Parameters Fractional Factorial Sampling Latin Hypercube Sampling Multivariate Stratified Sampling Quasi-random Sampling with Low-discrepancy Sequences Group Sampling Exercises Exercise Solutions 99 3 Elementary Effects Method Introduction The Elementary Effects Method The Sampling Strategy and its Optimization The Computation of the Sensitivity Measures Working with Groups The EE Method Step by Step Conclusions Exercises Solutions 3 4 Variance-based Methods Different Tests for Different Settings Why Variance? Variance-based Methods. ABrief History Interaction Effects Total Effects How to Compute the Sensitivity Indices 64

4 CONTENTS IX 4.7 FAST and Random Balance Designs Putting the Method to Work: The Infection Dynamics Model Caveats Exercises 74 5 Factor Mapping and Metamodelling 83 With Peter Young 5. Introduction Monte Carlo Filtering (MCF) Implementation of Monte Carlo Filtering Pros and Cons Exercises Solutions Examples Metamodelling and the High-Dimensional Model Representation Estimating HDMRs and Metamodels A Simple Example Another Simple Example Exercises Solutions to Exercises Conclusions Sensitivity Analysis: From Theory to Practice Example : A Composite Indicator Setting the Problem A Composite Indicator Measuring Countries' Performance in Environmental Sustainability Selecting the Sensitivity Analysis Method The Sensitivity Analysis Experiment and Results Conclusions Example 2: Importance of ]umps in Pricing Options Setting the Problem The Heston Stochastic Volatility Model with ]umps Selecting a Suitable Sensitivity Analysis Method The Sensitivity Analysis Experiment and Results Conclusions Example 3: A Chemical Reactor Setting the Problem Thermal Runaway Analysis of a Batch Reactor Selecting the Sensitivity Analysis Method 266

5 x CONTENTS The Sensitivity Analysis Experiment and Results Conclusions 6.4 Example 4: A Mixed Uncertainty-Sensitivity Plot 6.4. In Brief 6.5 When to use What? Afterword Bibliography Index