1IntroductiontoSensitivityAnalysis 1
1.1ModelsandSensitivityAnalysis 1
1.1.1Definition 1
1.1.2Models 2
1.1.3ModelsandUncertainty 3
1.1.4HowtoSetUpUncertaintyandSensitivity
Analyses 5
1.1.5ImplicationsforModelQuality 9
1.2MethodsandSettingsforSensitivityAnalysis–an
Introduction 10
1.2.1LocalversusGlobal 11
1.2.2ATestModel 12
1.2.3ScatterplotsversusDerivatives 13
1.2.4Sigma-normalizedDerivatives 15
1.2.5MonteCarloandLinearRegression 16
1.2.6ConditionalVariances–FirstPath 20
1.2.7ConditionalVariances–SecondPath 21
1.2.8ApplicationtoModel(1.3) 22
1.2.9AFirstSetting:‘FactorPrioritization’ 24
1.2.10NonadditiveModels 25
1.2.11Higher-orderSensitivityIndices 29
1.2.12TotalEffects 31
1.2.13ASecondSetting:‘FactorFixing’ 33
1.2.14RationaleforSensitivityAnalysis 34
1.2.15TreatingSets 36
1.2.16FurtherMethods 37
1.2.17ElementaryEffectTest 38
1.2.18MonteCarloFiltering 39
1.3NonindependentInputFactors 41
1.4PossiblePitfallsforaSensitivityAnalysis 41
1.5ConcludingRemarks 42
1.6Exercises 44
1.7Answers 44
1.8AdditionalExercises 50
1.9SolutionstoAdditionalExercises 51
2ExperimentalDesigns 53
2.1Introduction 53
2.2DependencyonaSingleParameter 55
2.3SensitivityAnalysisofaSingleParameter 58
2.3.1RandomValues 58
2.3.2StratifiedSampling 59
2.3.3MeanandVarianceEstimatesforStratified
Sampling 61
2.4SensitivityAnalysisofMultipleParameters 64
2.4.1LinearModels 65
2.4.2One-at-a-time(OAT)Sampling 66
2.4.3LimitsontheNumberofInfluentialParameters70
2.4.4FractionalFactorialSampling 71
2.4.5LatinHypercubeSampling 76
2.4.6MultivariateStratifiedSampling 80
2.4.7Quasi-randomSamplingwithLow-discrepancy
Sequences 82
Sequences 82
2.5GroupSampling 89
2.6Exercises 96
2.7ExerciseSolutions 99
3ElementaryEffectsMethod 109
3.1Introduction 109
3.2TheElementaryEffectsMethod 110
3.3TheSamplingStrategyanditsOptimization 112
3.4TheComputationoftheSensitivityMeasures 116
3.5WorkingwithGroups 121
3.6TheEEMethodStepbyStep 123
3.7Conclusions 127
3.8Exercises 128
3.9Solutions 131
4Variance-basedMethods 155
4.1DifferentTestsforDifferentSettings 155
4.2WhyVariance? 157
4.3Variance-basedMethods.ABriefHistory 159
4.4InteractionEffects 161
4.5TotalEffects 162
4.6HowtoComputetheSensitivityIndices 164
4.7FASTandRandomBalanceDesigns 167
4.8PuttingtheMethodtoWork:TheInfection
DynamicsModel 169
4.9Caveats 174
4.10Exercises 174
5FactorMappingandMetamodelling 183
WithPeterYoung
5.1Introduction 183
5.2MonteCarloFiltering(MCF) 184
5.2.1ImplementationofMonteCarloFiltering 185
5.2.2ProsandCons 187
5.2.3Exercises 189
5.2.4Solutions 190
5.2.5Examples 200
5.3MetamodellingandtheHigh-DimensionalModel
Representation 212
5.3.1EstimatingHDMRsandMetamodels 214
5.3.2ASimpleExample 224
5.3.3AnotherSimpleExample 227
5.3.4Exercises 229
5.3.5SolutionstoExercises 231
5.4Conclusions 235
6SensitivityAnalysis:FromTheorytoPractice 237
6.1Example1:ACompositeIndicator 238
6.1.1SettingtheProblem 238
6.1.2ACompositeIndicatorMeasuringCountries’
PerformanceinEnvironmentalSustainability239
6.1.3SelectingtheSensitivityAnalysisMethod 241
6.1.4TheSensitivityAnalysisExperimentand
Results 242
6.1.5Conclusions 252
6.2Example2:ImportanceofJumpsinPricingOptions253
6.2.1SettingtheProblem 253
6.2.2TheHestonStochasticVolatilityModel
withJumps 255
6.2.3SelectingaSuitableSensitivityAnalysisMethod258
6.2.4TheSensitivityAnalysisExperimentandResults258
6.2.5Conclusions 261
6.3Example3:AChemicalReactor 262
6.3.1SettingtheProblem 262
6.3.2ThermalRunawayAnalysisofaBatchReactor263
6.3.3SelectingtheSensitivityAnalysisMethod 266
6.3.4TheSensitivityAnalysisExperimentand
Results 266
6.3.5Conclusions 269
6.4Example4:AMixedUncertainty–SensitivityPlot 270
6.4.1InBrief 270
6.5WhentouseWhat? 272
Afterword 277
Bibliography 279
Index 287