A Statistical View of Uncertainty Quantification: Interface between Statistics and Applied Mathematics
Abstract
Because of the advances in complex mathematical models and fast computer codes, computer experiments have become popular in engineering and scientific investigations. Statisticians have worked on the design, modeling and computation aspects of computer experiments. Applied mathematicians have approached a closely related class of problem called UQ (uncertainty quantification). Interface between the two approaches is made in the talk. An exemplary problem on the statistical side is presented to illustrate this interface. Consider deterministic computer experiments with tuning parameters which determine the accuracy of the numerical algorithm (e.g., mesh density in finite element analysis). To efficiently integrate computer outputs with different tuning parameters, a class of nonstationary Gaussian process models consistent with the knowledge in numerical analysis is proposed to model the integrated output. Estimation is performed by using Bayesian computation. Numerical studies show the advantages of the proposed method over existing methods. A related problem is given to illustrate the interplay between modeling and design. For this and a broader class of models with multi-levels of fidelity, the nested space-filling designs are most suitable. Some examples are given and the underlying mathematics will be discussed.
About the speaker
Prof. Jeff Wu received his PhD in Statistics from the University of California at Berkeley in 1976. He was formerly the H. C. Carver Professor of Statistics and Professor of Industrial and Operations Engineering at the University of Michigan, the GM/NSERC Chair in Quality and Productivity at the University of Waterloo. He also taught in the Statistics Department at the University of Wisconsin. He is currently Professor in Industrial and Systems Engineering at Georgia Institute of Technology, where he holds the Coca-Cola Chair in Engineering Statistics.
Prof. Wu’s work is widely cited in professional journals as well as in magazines, including a feature article about his work in Canadian Business and a special issue of Newsweek on quality. He has served as editor or associate editor for several prestigious statistical journals like Annals of Statistics, Journal of American Statistical Association, Technometrics, and Statistica Sinica. He has published more than 130 research articles in peer-reviewed journals.
Prof. Wu is a Member of the US National Academy of Engineering, Academia Sinica, Honorary Professor at Chinese Academy of Sciences, and an Honorary Doctor of Mathematics at University of Waterloo. He is a Fellow of the American Society for Quality, Institute of Mathematical Statistics, and American Statistical Association. Prof Wu has won numerous awards, including the Committee of Presidents of Statistical Societies (COPSS) Presidents Award, Taiwan’s Pan Wenyuan Technology Award, the Wilcoxon Prize for the best paper in Technometrics, the Brumbaugh Award for the single most important paper to quality control among the publications sponsored by the American Society for Quality Control, and the Jack Youden Prize twice for best paper in Technometrics. He was the P. C. Mahalanobis Memorial Lecturer at the Indian Statistical Institutes with widely cited research work and a listing as an “ISI (Institute for Scientific Information) Highly Cited Researcher”.
* The lecture will be followed by a Center for Statistical Science Seminar:
A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties
Prof Rui Tuo, Chinese Academy of Sciences
Time: 4:15 pm
Venue: IAS Lecture Theater, Lo Ka Chung Building, Lee Shau Kee Campus, HKUST
