Computational Modeling by Case Study: All Models Are Uncertain

Mathematical models power the modern world; they allow us to design safe buildings, investigate changes to the climate, and study the transmission of diseases through a population. However, all models are uncertain: building contractors deviate from the planned design, humans impact the climate unpredictably, and diseases mutate and change. Modern advances in mathematics and statistics provide us with techniques to understand and quantify these sources of uncertainty, allowing us to predict and design with confidence.This book presents a comprehensive treatment of uncertainty: its conceptual nature, techniques to quantify uncertainty, and numerous examples to illustrate sound approaches. Several case studies are discussed in detail to demonstrate an end-to-end treatment of scientific modeling under uncertainty, including framing the problem, building and assessing a model, and answering meaningful questions. The book illustrates a computational approach with the Python package Grama, presenting fully reproducible examples that students and practitioners can quickly adapt to their own problems.

About the Author :
Zachary del Rosario is an assistant professor of engineering and applied statistics at Olin College (USA), an engineering college focused on pedagogical innovation. He received his PhD from Stanford University (USA) in 2020. Professor del Rosario is the maintainer of the software package Grama, and has used this software to teach advanced uncertainty quantification (UQ) techniques to undergraduate students. He has published several technical articles on UQ and statistics. Gianluca Iaccarino is the Director of the Institute for Computational Mathematical Engineering (USA) and a professor in the Mechanical Engineering Department at Stanford University (USA). He received his PhD at the Politecnico di Bari (Italy) and worked for several years at the Center for Turbulence Research (NASA Ames & Stanford, USA). He is the Director of the Predictive Science Academic Alliance Program Center at Stanford, funded by the US Department of Energy, which focusses on multiphysics simulations, uncertainty quantification and exascale computing. In 2010, he received the Presidential Early Career Award for Scientists and Engineers (PECASE) award.

Review :
"This is a book you'll want to read and re-read. The world is complicated enough that we must use models that we know are wrong. So how then do we reason about the resulting error? This book shows how to quantify uncertainty using probability and statistics, while not hiding the underlying philosophical problems. It is well illustrated with live examples from engineering and stories from real life."Art B. Owen Professor of Statistics, Stanford University'This book is outstanding as it provides, in an accessible way, impressive coverage of the three pillars of modern analytics. It can be used for self-learning, for academic courses and for workshops in industry. I highly recommend the book to practitioners, educators and students alike. They will benefit from its content, enjoy it style, learn new skills and gain new insights.'Ron S. KenettSenior Research Fellow at Technion - Israel Institute of Technology