CMSA Talk: Peter Qian

Title: Some Statistical Aspects of Uncertainty Quantification Abstract: Computer simulations, such as computational fluid dynamics, finite element analysis, agent-based models and multi-physics codes, are widely used in science, engineering and business for studying complex phenomena. As simulation models are never perfect and possess various uncertainties, including random initial condition and boundary conditions, input uncertainty and model discrepancy, uncertainty quantification (UQ) plays a big role in simulation-based decision-making. Without a rigorous mathematical framework for UQ in a simulation model, the simulation results and the consequent decision-making can be misleading. As statisticians, we all know the heart of statistics is the quantification of uncertainty. The motivation behind this talk is to discuss three statistical aspects of the emerging field of UQ. First, scalable design of experiments methods are developed to efficiently run complex simulations in parallel. These designs can be divided into slices and have a natural interface with high performance computing platforms. Second, a theoretical framework is introduced to investigate the statistical and numerical tradeoff of an approximation model for a black-box simulation code with Big Data. Guided by this framework, a sequential method called iKriging is introduced to build an accurate approximation model with a large number of observations. Third, a new statistical method is introduced to efficiently solve optimization under uncertainty problems. The key idea of the method is to embed negative dependence among batches to significantly reduce the variability of sample average approximations of a stochastic program. A number of examples will be used for illustrating the developed methods. (Colloquium: flyer and video)