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This book is an expository introduction to the methodology of sensitivity analysis of model output. It is primarily intended for investigators, students and researchers that are familiar with mathematical models but are less familiar with the techniques for performing their sensitivity analysis. A variety of sensitivity methods have been developed over the years. This monograph helps the analyst in her/his first exploration of this world. The main goal of is to foster the recognition of the crucial role of sensitivity analysis methods as the techniques that allow us to gain insights from quantitative models. Also, exercising rigor in performing sensitivity analysis becomes increasingly relevant both to decision makers and modelers. The book helps the analyst in structuring her/his sensitivity analysis quest properly, so that to obtain the correct answer to the corresponding managerial question.

The first part of the book covers Deterministic Methods, including Tornado Diagrams; One-Way Sensitivity Analysis; Differentiation-Based Methods and Local Sensitivity Analysis with Constraints. The second part looks at Probabilistic Methods, including Regression-based methods, Variance-Based Methods, and Distribution-based methods. The final section looks at Applications, including capital budgeting, sensitivity analysis in climate change modelling and in the risk assessment of a lunar space mission.



Chapter 1. Decisions and Sensitivity Analysis

We are living in a new era on the verge of a data-driven economy.
Emanuele Borgonovo

Chapter 2. Setup of Sensitivity Analysis

This section is devoted to the most important step in sensitivity analysis, the formulation of the sensitivity question. Scientists have developed myriads of models in different disciplines, and there are myriads of sensitivity analysis methods waiting to be used to explore the content of those models.
Emanuele Borgonovo

Deterministic Methods


Chapter 3. Tornado Diagrams

A sensitivity analysis method is deterministic if it does not require the analyst to specify a distribution for the model inputs .
Emanuele Borgonovo

Chapter 4. One-Way Sensitivity Functions

Tornado diagrams provide indications about the sensitivity of the model output to one-at-a-time model-input variations at their extreme ranges.
Emanuele Borgonovo

Chapter 5. Differentiation-Based Methods

Methods based on differentiation represent an important class of probabilistic sensitivity methods.
Emanuele Borgonovo

Chapter 6. An Application: Classical Optimization

The solution of several problems in operations research and the managerial sciences leads to classic optimization models.
Emanuele Borgonovo

Chapter 7. From Infinitesimal to Finite Changes: Generalized Tornado Diagrams

This chapter proposes a unified view of three additional deterministic methods: scenario analysis, functional ANOVA decomposition and finite change sensitivity indices. We start with scenario analysis.
Emanuele Borgonovo

Chapter 8. Estimation and a Computational Shortcut

The complete dissection of a finite change requires \(2^{n}-1\) model evaluations, which is the number of finite change sensitivity indices of all orders.
Emanuele Borgonovo

Chapter 9. Multilinear Functions: Taylor Versus Functional ANOVA Expansions

In this section, we present an analysis of the interaction properties of multilinear functions . Our aim is to show that, for a multilinear function, the integral (functional ANOVA) and Taylor expansions coincide.
Emanuele Borgonovo

Chapter 10. What to Use and When

Given our discussion of the various methods above, a natural question is: What is the (best) method to use? We phrase this question with “best” in parentheses because we do not believe that there is an absolutely “best sensitivity method”. In fact, even the answer to the simpler question “of which method should be used” is multifaceted.
Emanuele Borgonovo

Chapter 11. Value of Information

This section investigates the concept of expected value of perfect information. The definition we present here is the definition used in classical decision-analysis courses for decision making under risk.
Emanuele Borgonovo

Chapter 12. Local Sensitivity Analysis with Constraints

This chapter, which is our last on deterministic methods, addresses the removal of a typical assumption in sensitivity analysis.
Emanuele Borgonovo

Probabilistic Sensitivity Methods


Chapter 13. Uncertainty Quantification

The importance of properly displaying the analyst/decision maker’s degree of belief about the problem at hand is recognized by several agencies and international institutions.
Emanuele Borgonovo

Chapter 14. Global Sensitivity Analysis

After completing an uncertainty analysis , the next step is a global sensitivity analysis .
Emanuele Borgonovo

Chapter 15. Variance-Based Methods

As a way of introducing variance-based methods , we could ask the following question: Is it possible to introduce sensitivity indicators that explain the variance of the model output rather than only the fraction of the variance associated with the linear surrogate model? The answer is found in variance-based sensitivity measures, which we describe next.
Emanuele Borgonovo

Chapter 16. The —Importance Measure

Sensitivity measures that consider the output’s entire distribution function are called moment-independent measures. In recent years, the amount of attention paid to moment-independent sensitivity measures has grown.
Emanuele Borgonovo

Chapter 17. CDF-Based Sensitivity Measures

Baucells and Borgonovo (2013) introduce and analyze global sensitivity measures based on cumulative distribution functions (CDFs).
Emanuele Borgonovo

Chapter 18. Transformation Invariant Sensitivity Measures

Transformation invariance is a particularly interesting property when analyzing the sensitivity of model output.
Emanuele Borgonovo

Chapter 19. Global Sensitivity Analysis with Value of Information

All of the sensitivity measures that have been defined thus far are measures of value sensitivity. In other words, they measure the change in value (or distribution) of the model output Y as we obtain information about \(X_{i}.\)
Emanuele Borgonovo

Chapter 20. Exercising Global Sensitivity Analysis: Test Cases

The purpose of this section it to introduce a series of analytical test cases in which the sensitivity measures illustrated thus far can be obtained analytically.
Emanuele Borgonovo

Chapter 21. Additional Results on the Analytical Properties of High-Dimensional Model Representations

Before we come to the application section, we address some additional properties of the functional ANOVA expansion.
Emanuele Borgonovo



Chapter 22. Case Studies

We start with the application of local sensitivity analysis to capital budgeting .
Emanuele Borgonovo


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