Computer models are found to be effective in many applications such as climate modeling, human organ modeling, and nuclear physics problems. There is an increasing interest how the computer output could be coupled with locally available data for quick inference that accounts for the myriad of uncertainty sources. This project will develop new computational techniques and flexible model building in addition to associated software development. The project will impact science and society because of the interdisciplinary research between nuclear physics, computer modeling, and statistical theory. This research will uncover statistical properties and computational techniques to transform the next generation computational scientists and practitioners. The fast and scalable computation will enhance the use of computer models in real world problem solving.

This project develops statistically valid techniques that are both computationally inexpensive and practical to facilitate the use of computer model outputs together with local data accounting model and parameter uncertainty. The approach extends to a robust modeling approach in case of model failures that can occur when covering a large study domain. In particular, the investigators develop Gaussian process-based emulator that models both the sparsely observed computer model and the unknown discrepancy that explains the gap between the model and reality. The approach is Bayesian which provides for the natural quantification of uncertainties. The key tool for statistical inference is to replace the standard practice of Markov Chain Monte Carlo (MCMC) with a novel usage of variational Bayes (VB) inference. While the variational Bayes is popular in machine learning literature, the technique is not as popular in statistics as MCMC based sampling techniques. The slow uptake the VB framework seems to be due to the additional complexities it adds to modeling and the relatively uncharted theoretical properties. This project will develop an innovative VB algorithm to resolve the present issues in computer model calibration with the aim of improving the computation scalability and extendibility in a robust modeling approach. The investigators plan to build software for translational research to reach the desired applications for maximum impact. The research will provide transformative research that impacts statistical computation, Bayesian statistics, computer modeling and calibration, and related applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Yong Zeng
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Michigan State University
East Lansing
United States
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