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.
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