Montana Workshop on Uncertainty Quantification, June 2015; The University of Montana, Missoula, MT

University Of Montana, Missoula MT

Investigators

Abstract

Montana Workshop on Uncertainty Quantification, University of Montana, June 24-26, 2015 Developments in high-performance computing in the last decade have enabled tremendous advances in applied mathematics and physics, in large part because today's computers allow scientists to solve problems that couldn't before even be attempted. Many of the fields that are advancing the most quickly impact Americans' daily lives, including radiation detection interrogation and analysis techniques for national security science, medical advances through new imaging techniques, and weather modeling and prediction. In the science of the 21st-century, solving difficult problems is not enough; scientists must also make statistically justifiable statements about the uncertainties in their solutions. Uncertainty Quantification (UQ) is a burgeoning field that sits at the interface of computation, applied mathematics, physics, and statistics, and its goal is to extend and develop statistical methods to assign meaningful error bars and uncertainty estimates to the solutions of computationally challenging applied mathematics and physics problems. The Montana Workshop on Uncertainty Quantification will gather top experts and talented young researchers in the field to the University of Montana to develop and disseminate the latest theory, techniques, and applications of uncertainty quantification. Uncertainty quantification (UQ) denotes the science of incorporating statistical methods into the problem of fitting physics-based mathematical models to physical systems, with the ultimate goal of obtaining theoretically justifiable error bars for model predictions and for estimates of model parameters. A few of the physical systems that will be discussed in the Montana Workshop on Uncertainty Quantification (MUQ) are high energy radiography in the security sciences, interferometry, data assimilation in weather modeling, astronomical imaging, medical imaging, process tomography, and control theory. Most of these applications are so-called inverse problems, which involve the estimation of parameters in a mathematical model of a physical system from finite dimensional measurements of output from that system. The unknown parameters are typically high-dimensional, resulting in an over-parameterized statistical model and hence high uncertainties in model predictions and in estimates of model parameters. Since such problems pose a particular challenge for traditional statistical techniques, the practice of UQ for inverse problems provides a rich source of new and important research problems in UQ and, as such, is one of the primary focuses of MUQ. The class of applications and research problems covered by the workshop will be broad, from the very applied (e.g., estimating object densities from real data in high-energy radiography experiments) to the very theoretical (e.g., an analysis of a specific Bayesian approach for solving an inverse problem in the function space setting). In this workshop, researchers specializing in theory, computation, and applications will come together to share the latest techniques and advances in UQ. More details about the workshop can be found at http://www.math.umt.edu/bardsley/MUQ/MUQ.html.