UBC Theses and Dissertations
Design and analysis of computer experiments : assessing and advancing the state of the art Chen, Hao
Computer experiments have been widely used in practice as important supplements to traditional laboratory-based physical experiments in studying complex processes. However, a computer experiment, which in general is based on a computer model with limited runs, is expensive in terms of its computational time. Sacks.et.al. (1989) proposed to use Gaussian process (GP) as a statistical surrogate, which has become a standard way to emulate a computer model. In the thesis, we are concerned with design and analysis of computer experiments based on a GP. We argue that comprehensive, evidence-based assessment strategies are needed when comparing different model options and designs. We first focus on the regression component and the correlation structure of a GP. We use comprehensive assessment strategies to evaluate the effect of the two factors on the prediction accuracy. We also have a limited evaluation on empirical Bayes methods and full Bayes methods, from which we notice Bayes methods with a squared exponential structure do not yield satisfying prediction accuracy in some examples considered. Hence, we propose to use hybrid and full Bayes methods with flexible structures. Through empirical studies, we show the new Bayes methods with flexible structures not only have better prediction accuracy, but also have a better quantification of uncertainty. In addition, we are interested in assessing the effect of design on prediction accuracy. We consider a number of popular designs in the literature and use several examples to evaluate their performances. It turns out the performance difference between designs is small for most of the examples considered. From the evaluation of designs, we are motivated to use a sequential design strategy. We compare the performances of two existing sequential search criteria and handle several important issues in using the sequential design to estimate an extreme probability/quantile of a floor supporting system. Several useful recommendations have also been made.
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