Large sets of coupled, nonlinear equations arise in a number of disciplines in connection with computer based models of physical, social and economic processes. Solutions for such large systems of equations must be effected by means of digital computers using appropriately designed codes. This paper addresses itself to the critically important problem of how sensitive the solutions are to variations of, or inherent uncertainties in, the parameters of the equation set. We review here, and also present further developments, of our statistical method of sensitivity analysis. The sensitivity analysis presented here is nonlinear and thus permits one to study the effects of large deviations from the nominal parameter values. In addition, since all parameters are varied simultaneously, one can explore regions of parameter space where several parameters deviate simultaneously from their nominal values. Developed her eis a theory of a method of sensitivity analysis, then detail the method of implementation and finally present several examples of its use to date.

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.

Sensitivity Analysis in Earth Observation Modeling highlights the state-of-the-art in ongoing research investigations and new applications of sensitivity analysis in earth observation modeling. In this framework, original works concerned with the development or exploitation of diverse methods applied to different types of earth observation data or earth observation-based modeling approaches are included. An overview of sensitivity analysis methods and principles is provided first, followed by examples of applications and case studies of different sensitivity/uncertainty analysis implementation methods, covering the full spectrum of sensitivity analysis techniques, including operational products. Finally, the book outlines challenges and future prospects for implementation in earth observation modeling. Information provided in this book is of practical value to readers looking to understand the principles of sensitivity analysis in earth observation modeling, the level of scientific maturity in the field, and where the main limitations or challenges are in terms of improving our ability to implement such approaches in a wide range of applications. Readers will also be informed on the implementation of sensitivity/uncertainty analysis on operational products available at present, on global and continental scales. All of this information is vital in the selection process of the most appropriate sensitivity analysis method to implement. Outlines challenges and future prospects of sensitivity analysis implementation in earth observation modeling Provides readers with a roadmap for directing future efforts Includes case studies with applications from different regions around the globe, helping readers to explore strengths and weaknesses of the different methods in earth observation modeling Presents a step-by-step guide, providing the principles of each method followed by the application of variants, making the reference easy to use and follow