Sensitivity analysis should be considered a pre-requisite for statistical model building in any scientific discipline where modelling takes place. For a non-expert, choosing the method of analysis for their model is complex, and depends on a number of factors. This book guides the non-expert through their problem in order to enable them to choose and apply the most appropriate method. It offers a review of the state-of-the-art in sensitivity analysis, and is suitable for a wide range of practitioners. It is focussed on the use of SIMLAB – a widely distributed freely-available sensitivity analysis software package developed by the authors – for solving problems in sensitivity analysis of statistical models. Other key features: Provides an accessible overview of the current most widely used methods for sensitivity analysis. Opens with a detailed worked example to explain the motivation behind the book. Includes a range of examples to help illustrate the concepts discussed. Focuses on implementation of the methods in the software SIMLAB - a freely-available sensitivity analysis software package developed by the authors. Contains a large number of references to sources for further reading. Authored by the leading authorities on sensitivity analysis.

A text surveying perturbation techniques and sensitivity analysis of linear systems is an ambitious undertaking, considering the lack of basic comprehensive texts on the subject. A wide-ranging and global coverage of the topic is as yet missing, despite the existence of numerous monographs dealing with specific topics but generally of use to only a narrow category of people. In fact, most works approach this subject from the numerical analysis point of view. Indeed, researchers in this field have been most concerned with this topic, although engineers and scholars in all fields may find it equally interesting. One can state, without great exaggeration, that a great deal of engineering work is devoted to testing systems' sensitivity to changes in design parameters. As a rule, high-sensitivity elements are those which should be designed with utmost care. On the other hand, as the mathematical modelling serving for the design process is usually idealized and often inaccurately formulated, some unforeseen alterations may cause the system to behave in a slightly different manner. Sensitivity analysis can help the engineer innovate ways to minimize such system discrepancy, since it starts from the assumption of such a discrepancy between the ideal and the actual system.

The book is organized into four chapters. The first three treat distinct types of design variables, and the fourth presents a built-up structure formulation that combines the other three. The first chapter treats finite-dimensional problems, in which the state variable is a finite-dimensional vector of structure displacements and the design parameters. The structual state equations are matrix equations for static response, vibration, and buckling of structures and matrix differential equations for transient dynamic response of structures, which design variables appearing in the coefficient matrices.

This book provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties. The authors use a practical point of view and real case studies as well as numerous examples, and applications of the different approaches are illustrated throughout using R code to explain their usage and usefulness in practice. Basics and Trends in Sensitivity Analysis: Theory and Practice in R covers a lot of material, including theoretical aspects of Sobol’ indices as well as sampling-based formulas, spectral methods, and metamodel-based approaches for estimation purposes; screening techniques devoted to identifying influential and noninfluential inputs; variance-based measures when model inputs are statistically dependent (and several other approaches that go beyond variance-based sensitivity measures); and a case study in R related to a COVID-19 epidemic model where the full workflow of sensitivity analysis combining several techniques is presented. This book is intended for engineers, researchers, and undergraduate students who use complex numerical models and have an interest in sensitivity analysis techniques and is appropriate for anyone with a solid mathematical background in basic statistical and probability theories who develops and uses numerical models in all scientific and engineering domains.

Artificial neural networks are used to model systems that receive inputs and produce outputs. The relationships between the inputs and outputs and the representation parameters are critical issues in the design of related engineering systems, and sensitivity analysis concerns methods for analyzing these relationships. Perturbations of neural networks are caused by machine imprecision, and they can be simulated by embedding disturbances in the original inputs or connection weights, allowing us to study the characteristics of a function under small perturbations of its parameters. This is the first book to present a systematic description of sensitivity analysis methods for artificial neural networks. It covers sensitivity analysis of multilayer perceptron neural networks and radial basis function neural networks, two widely used models in the machine learning field. The authors examine the applications of such analysis in tasks such as feature selection, sample reduction, and network optimization. The book will be useful for engineers applying neural network sensitivity analysis to solve practical problems, and for researchers interested in foundational problems in neural networks.

The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists. Sensitivity analysis is used to ascertain how a given model output depends upon the input parameters. This is an important method for checking the quality of a given model, as well as a powerful tool for checking the robustness and reliability of its analysis. The topic is acknowledged as essential for good modelling practice and is an implicit part of any modelling field. Offers an accessible introduction to sensitivity analysis. Covers all the latest research. Illustrates concepts with numerous examples, applications and case studies. Includes contributions from the leading researchers active in developing strategies for sensitivity analysis. The principles of sensitivity analysis are carefully described and suitable methods for approaching many types of problems are given. The book introduces the modeller to the entire casual assessment chain, from data to predictions, whilst explaining the impact of source uncertainties and framing assumptions. A ‘hitch-hikers guide’ is included to allow the more experienced reader to readily access specific applications. Modellers from a wide range of disciplines, including biostatistics, economics, environmental impact assessment, chemistry and engineering will benefit greatly from the numerous examples and applications. "Presents many different sensitivity analysis methodologies and demonstrates their usefulness in scientific research." (Zentralblatt MATH)

As computer-assisted modeling and analysis of physical processes have continued to grow and diversify, sensitivity and uncertainty analyses have become indispensable investigative scientific tools in their own right. While most techniques used for these analyses are well documented, there has yet to appear a systematic treatment of the method based