Elementary effects method

Abstract: Preface. 1. Introduction to Sensitivity Analysi. 1.1 Models and Sensitivity Analysis. 1.1.1 Definition. 1.1.2 Models. 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. 1.6 Exercises. 1.7 Answers. 1.8 Additional Exercises. 1.9 Solutions to Additional Exercises. 2. Experimental Designs. 2.1 Introduction. 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. 2.6 Exercises. 2.7 Exercise Solutions. 3. Elementary Effects Method. 3.1 Introduction. 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. 3.7 Conclusions. 3.8 Exercises. 3.9 Solutions. 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. 4.9 Caveats. 4.10 Exercises. 5. Factor Mapping and Metamodelling. 5.1 Introduction. 5.2 Monte Carlo Filtering (MCF). 5.2.1 Implementation of Monte Carlo Filtering. 5.2.2 Pros and Cons. 5.2.3 Exercises. 5.2.4 Solutions. 5.2.5 Examples. 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. 5.3.4 Exercises. 5.3.5 Solutions to Exercises. 5.4 Conclusions. 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. 6.1.5 Conclusions. 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. 6.2.5 Conclusions. 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. 6.3.5 Conclusions. 6.4 Example 4: a Mixed Uncertainty-Sensitivity Plot. 6.4.1 In Brief. 6.5 When to use What? Afterword. Bibliography. Index.

Abstract: A computational model is a representation of some physical or other system of interest, first expressed mathematically and then implemented in the form of a computer program; it may be viewed as a function of inputs that, when evaluated, produces outputs. Motivation for this article comes from computational models that are deterministic, complicated enough to make classical mathematical analysis impractical and that have a moderate-to-large number of inputs. The problem of designing computational experiments to determine which inputs have important effects on an output is considered. The proposed experimental plans are composed of individually randomized one-factor-at-a-time designs, and data analysis is based on the resulting random sample of observed elementary effects, those changes in an output due solely to changes in a particular input. Advantages of this approach include a lack of reliance on assumptions of relative sparsity of important inputs, monotonicity of outputs with respect to inputs, or ad...