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theses

Computer experiments refer to the study of real systems using complex mathematical models. They have been widely used as alternatives to physical experiments, especially for studying complex systems in science and engineering. Typically, computer experiments require a great deal of time and computing to conduct and they are nearly deterministic in the sense that a particular input will produce almost the same output if given to the computer experiment on another occasion. Therefore, it is desirable to build an interpolator for computer experiment outputs and use it as an emulator for the actual computer experiment. This thesis mainly focuses on building efficient statistical emulators for computer experiments and providing prediction uncertainty with real-world applications.
Gaussian process (GP) models are widely used in the analysis of computer experiments. However, two issues have not been solved satisfactorily. One is the computational issue that hinders GP from broader application, especially for massive data with high-dimensional inputs. The other is the underestimation of prediction uncertainty in GP modeling. To tackle these problems simultaneously, in Chapter 1 we propose two methods to construct GP predictive distributions based on a new version of bootstrap subsampling. The new subsampling procedure borrows the strength of space-filling designs to provide an efficient subsample and thus reduce the computational complexity. It is shown that this procedure not only alleviates the computational difficulty in GP modeling, but also provides unbiased predictors with better quantifications of uncertainty comparing with existing methods. We illustrate the proposed methods by two complex computer experiments with high-dimensional inputs and tens of thousands of simulation outputs.
Traditional GP models are limited in the computational capability of dealing with massive and complex data. To overcome the computational issue without imposing strong assumptions, a spline-based approach is developed to build emulators for computer experiments to handle big spatial-temporal data in Chapter 2. A direct application of the proposed framework is to model Antarctic ice-sheet contributions to sea level rise. Sea level rise is expected to impact millions of people in coastal communities in the coming centuries. Global, regional, and local sea level rise projections are highly uncertain, partially due to uncertainties in Antarctic ice-sheet (AIS) dynamics, and parameterized simulations are expensive to run. We create an ice-sheet emulator to provide near-continuous distributions of the sea-level equivalent of AIS melt based on two input parameters, which alter the behavior AIS mass loss, under two forcing scenarios: the Last Interglacial and RCP 8.5 forcing. The spline-based emulator with Gaussian Process priors on the spline parameters is flexible enough to capture the nonlinearity of the underlying structure, while computationally feasible at the same time. It achieves a good fit for the physical model and provides prediction uncertainties simultaneously.

ETD_9773

Ph.D.

Includes bibliographical references

doi:10.7282/t3-7m6x-6j14

ETD doctoral

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