Quantifying Uncertainty in Scientific and Engineering Models

Every scientific model of the physical world carries inherent uncertainty, yet making reliable decisions requires us to measure and manage this unpredictability. This text-based course provides a clear, foundational pathway to understanding how uncertainty behaves and how to mathematically account for it in your analysis. You will transition from basic probability concepts to implementing robust computational methods that quantify risk and variability in complex systems. What you'll learn: - Understand the foundational theory of probability, random variables, and sources of model uncertainty - Represent uncertainty using modern statistical distributions and parametric models - Apply Monte Carlo sampling techniques and modern Markov Chain Monte Carlo algorithms to explore parameter spaces - Propagate uncertainty through physical and mathematical models to predict outcome distributions - Update model parameters with observational data using Bayesian inference principles - Practice evaluating model sensitivity to identify which inputs drive the most uncertainty We begin by establishing essential definitions, core mathematical frameworks, and the philosophy of uncertainty. Next, we guide you through practical computational techniques, coupling theoretical methodology with structured written exercises and step-by-step code implementations to help you apply these concepts to real-world scientific and engineering problems. This course is designed for beginners, students, and practitioners in science, engineering, and data analysis who want a solid mathematical and practical introduction to uncertainty quantification. No advanced background in probability is required to start. Begin reading today to build more reliable, risk-aware models for your scientific and engineering projects.