Global Sensitivity Analysis The Primer

by Saltelli, Andrea; Ratto, Marco; Andres, Terry; Campolongo, Francesca; Cariboni, Jessica; Gatelli, Debora; Saisana, Michaela; Tarantola, Stefano

• ISBN13: 9780470059975
• ISBN10: 0470059974
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-02-11
• Publisher: Wiley-Interscience

Summary

Complex mathematical and computational models are used in all areas of society and technology and yet model based science is increasingly contested or refuted, especially when models are applied to controversial themes in domains such as health, the environment or the economy. More stringent standards of proofs are demanded from model-based numbers, especially when these numbers represent potential financial losses, threats to human health or the state of the environment. Quantitative sensitivity analysis is generally agreed to be one such standard.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.The book: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.

Author Biography

Andrea Saltelli, Francesca Campolongo, Jessica Cariboni, Debora Gatelli, Fulvia Pennoni, Marco Ratto,  Michaela Saisana, Stefano Tarantola – Joint Research Centre of the European Commission, Ispra, Unit of Applied Statistics and Econometrics.
Presently leading the Econometric and Applied Statistics Unit of the Joint Research Centre, lead author Professor Saltelli has published many articles in numerous journals over the last 30 years. He is also the main author and main editor of two previous books (both for Wiley).
Terry Andres – Department of Computer Science, University of Manitoba.
Dr Andres is one of the few people to successfully develop a graduate level sensitivity analysis course. He has delivered numerous courses to both students and practitioners and is an expert in experimental design.

Table of Contents

Preface

Introduction to Sensitivity Analysi

Models and Sensitivity Analysis

Definition

Models

Models and Uncertainty

How to Set Up Uncertainty and Sensitivity Analyses

Implications for Model Quality

Methods and Settings for Sensitivity Analysis - An Introduction

Local versus Global

A Test Model

Scatterplots versus Derivatives

Sigma-normalized Derivatives

Monte Carlo and Linear Regression

Conditional Variances - First Path

Conditional Variances - Second Path

Application to Model (3)

A First Setting: 'Factor Prioritization'

Nonadditive Models

Higher-order Sensitivity Indices

Total Effects

A Second Setting: 'Factor Fixing'

Rationale for Sensitivity Analysis

Treating Sets

Further Methods

Elementary Effect Test

Monte Carlo Filtering

Nonindependent Input Factors

Possible Pitfalls for a Sensitivity Analysis

Concluding Remarks

Exercises

Answers

Additional Exercises

Solutions to Additional Exercises

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

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

Variance-based Methods

Different Tests for Different Settings

Why Variance?

Variance-based Methods. A Brief History

Interaction Effects

Total Effects

How to Compute the Sensitivity Indices

FAST and Random Balance Designs

Putting the Method to Work: the Infection Dynamics Model

Caveats

Exercises

Factor Mapping and Metamodelling

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 1: 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 its Results

Conclusions

Example 2: Importance of Jumps in Pricing Options

Setting the Problem

The Heston Stochastic Volatility Model with Jumps

Selecting a Suitable Sensitivity Analysis Method

The Sensit

Table of Contents provided by Publisher. All Rights Reserved.