University of Warwick
Uncertainty quantification (UQ) is an interesting, fast growing research area aiming at developing methods to address, characterize and minimize the impact of parameter, data and model uncertainty in complex systems. Applications of uncertainty quantification include all areas of engineering, environmental, physical and biological systems, e.g., groundwater flow problems, shape uncertainties in aerodynamic applications or nano-optics, biochemical networks and finance. The efficient treatment of uncertainties in mathematical models requires ideas and tools from various disciplines including numerical analysis, statistics, probability and computational science. In this course, we will focus on the identification of parameters through observations of the response of the system - the inverse problem. The uncertainty in the solution of the inverse problem will be described via the Bayesian approach. We will derive Bayes' theorem in the infinite dimensional setting and discuss properties such as well-posedness, statistical estimates and connections to classical regularization methods. The second part of this course will be devoted to algorithms for the efficient approximation of the solution of the Bayesian inverse problem.