IMA New Directions Short Course

Science and engineering rely on links between data and mathematical and statistical models to understand or predict the behavior of complex systems. But data are usually subject to uncertainty, as are model parameters and even model structure. In many application areas it is essential that predictions based on models and data take these uncertainties into account. The topic of uncertainty quantification (UQ) includes mathematical and statistical methods that address the modeling, assessment, propagation, and management of uncertainties. The modeling of uncertainty typically relies on probability theory, while the interaction between models, data, and decisions can be cast in a statistical framework. More broadly, UQ draws upon many foundational ideas and techniques in mathematics and statistics (e.g., approximation theory, error estimation, statistical inference, stochastic modeling, and Monte Carlo methods) and applies these techniques to complex models using efficient computational approaches.

The objective of this summer school on Uncertainty Quantification and its Applications is to present an accessible introduction to the basic tools of uncertainty quantification, with the goal of orienting attendees to the field and helping them address UQ questions in their application areas of interest. Lectures will provide basic introductions to probability and stochastic processes, data analysis, estimation and inference, sensitivity analysis, uncertainty propagation, sampling methods, Bayesian computation, experimental design, and model validation. In addition, several guest lecturers will present a diverse set of applications and snapshots of current research, in which uncertainty quantification plays an important role.