Prediction and Calibration Using Outputs from Multiple Computer Simulators

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Computer Experiments
Hierarchical Model
Markov Chain Monte Carlo
Sequential Design

Computer simulators are widely used to describe and explore physical processes. In some cases, several simulators, which can be of different or similar fidelities, are available for this task. A big part of this thesis focuses on combining observations and model runs from multiple computer simulators to build a predictive model for the real process. The resulting models can be used to perform sensitivity analysis for the system, solve inverse problems and make predictions. The approaches are Bayesian and are illustrated through a few simple examples, as well as a real application in predictive science at the Center for Radiative Shock Hydrodynamics at the University of Michigan. Although the computer model can be viewed as an inexpensive way to gain insight into the physical process, it can become computationally expensive continuously exercise the computer simulator. A sequential design strategy is proposed to minimize the total number of function evaluations for finding the global extremum. The practical implementation of the proposed approach is addressed and applied to several examples containing multiple computer codes.

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Derek Bingham
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Thesis) Ph.D.