Sensitivity Analysis : An Introduction for the Management Scientist.
- 1st ed.
- 1 online resource (291 pages)
- International Series in Operations Research and Management Science Series ; v.251 .
- International Series in Operations Research and Management Science Series .
Intro -- Foreword -- Preface -- Contents -- 1 Decisions and Sensitivity Analysis -- 2 Setup of Sensitivity Analysis -- Part I Deterministic Methods -- 3 Tornado Diagrams -- 3.1 The Underlying Intuition -- 3.1.1 Formal Treatment: First-Order Sensitivity Measures -- 3.1.2 Algorithmic Implementation -- 3.1.3 Managerial Insights and Limitations -- 4 One-Way Sensitivity Functions -- 4.1 Algorithmic Implementation -- 4.2 Multilinear Models -- 4.3 General Relationship Between One-Way Sensitivity Functions and Tornado Diagrams -- 4.4 Do One-Way Sensitivity Functions Remedy the Limitations of Tornado Diagrams? -- 4.5 Managerial Insights -- 5 Differentiation-Based Methods -- 5.1 Managerial Insights and Limitations -- 5.2 Estimation -- 5.3 Multilinear Functions -- 5.4 The Implicit Function Framework and Samuelson's Comparative Statics -- 6 An Application: Classical Optimization -- 6.1 A Numerical Illustration -- 7 From Infinitesimal to Finite Changes: Generalized Tornado Diagrams -- 7.1 Scenario Analysis -- 7.2 Decomposition of Finite Changes -- 7.3 Generalized Tornado Diagrams and Managerial Insights -- 8 Estimation and a Computational Shortcut -- 8.1 The Mathematical Framework. First Step: Functional ANOVA -- 8.1.1 The Mathematical Framework Second Step: Finite Change Sensitivity Indices -- 8.1.2 Completing the Mathematical Framework: Small Changes -- 8.1.3 Normalized Finite Change Sensitivity Indices -- 9 Multilinear Functions: Taylor Versus Functional ANOVA Expansions -- 9.1 A Reliability Theory Implication -- 9.2 An Application -- 9.3 Finite Change Sensitivity Indices for Model Input Groups -- 10 What to Use and When -- 11 Value of Information -- 11.1 Premise -- 11.1.1 The Underlying Intuition -- 11.1.2 A More Formal Treatment -- 11.1.3 Managerial Insights -- 12 Local Sensitivity Analysis with Constraints. 12.1 A Generalized Rationale for the Differential Sensitivity of Model Output Under Constraints -- 12.2 Some Examples of Models with Input Constraints -- 12.3 A Numerical Example -- Part II Probabilistic Sensitivity Methods -- 13 Uncertainty Quantification -- 13.1 Numerical Uncertainty Propagation -- 13.2 Managerial Insights -- 14 Global Sensitivity Analysis -- 14.1 Regression-Based Methods -- 14.2 Regression-Based Methods with Rank Transformation -- 14.3 Managerial Insights -- 14.4 Impact of the Regression Fit -- 14.5 Properties -- 14.6 Summary -- 15 Variance-Based Methods -- 15.1 Historical Development -- 15.2 Functional ANOVA and Variance-Based Sensitivity Indices -- 15.3 Managerial Insights -- 15.4 Computational Cost -- 15.4.1 The Cost of a Brute-Force Estimation -- 15.4.2 The FAST Method -- 15.4.3 The Homma-Saltelli-Sobol Pick-and-freeze Design -- 15.4.4 Given-Data Estimation -- 15.5 Properties of Variance-Based Sensitivity Measures -- 15.6 Correlations -- 15.7 Variance and Uncertainty -- 16 The δ---Importance Measure -- 16.1 Properties -- 16.2 A Supplementary Viewpoint -- 16.3 An Example -- 16.4 Estimation -- 16.5 Managerial Interpretation -- 17 CDF-Based Sensitivity Measures -- 17.1 Relationships Between the Kuiper Metric and the L1 Norm -- 17.2 Estimation of CDF-Based Sensitivity Measures -- 17.3 Managerial Insights -- 18 Transformation Invariant Sensitivity Measures -- 18.1 Transformation Invariance from a Conceptual Viewpoint -- 18.2 Transformation Invariance: A Relevant Computational Advantage -- 18.3 Classes of Transformation-Invariant Separations -- 19 Global Sensitivity Analysis with Value of Information -- 19.1 Estimation -- 19.2 Managerial Insights -- 19.3 Variance- and Kullback-Leibler-Based Sensitivity Measures as Value-of-Information Sensitivity Measures -- 20 Exercising Global Sensitivity Analysis: Test Cases. 20.1 Normal Random Variables and Additive Model Output -- 20.2 Lognormal Random Variables and Multiplicative Model Output -- 20.3 Uniform Random Variables and Additive Model Output -- 20.4 A Non Additive and Non-multiplicative Model -- 21 Additional Results on the Analytical Properties of High-Dimensional Model Representations -- 21.1 Direction of Change -- 21.2 Managerial Insights -- 21.3 Ultramodularity -- Part III Applications -- 22 Case Studies -- 22.1 Local Sensitivity Analysis in Capital Budgeting -- 22.2 Determining Interactions in Complex Models: A Space PSA Application -- 22.2.1 The Space PSA Model -- 22.2.2 PSA Models as Multilinear Functions -- 22.2.3 Interactions at the Basic Event Level -- 22.2.4 Interactions at the System Level -- 22.2.5 Determining the Interaction Threshold -- 22.3 Uncertainty Analysis in Climate Change Modelling -- 22.4 Uncertainty Analysis in Business Planning: The Genzyme/GelTeX Joint Venture -- References -- Index.