| Summary: | Gaussian Processes (GPs) are commonly used in the analysis of data from a computer experiment. Ideally, the analysis will provide accurate predictions with correct coverage probabilities of credible intervals. A Bayesian method can, in principle, capture all sources of uncertainty and hence give valid inference. Several implementations are available in the literature, differing in choice of priors, etc. In this thesis, we first review three popular Bayesian methods in the analysis of computer experiments. Two prediction criteria are proposed to measure both the prediction accuracy and the prediction actual coverage probability. From a simple example, we notice that the performances of the three Bayesian implementations are quite different. Motivated by the performance difference, we specify four important factors in terms of Bayesian analysis and allocate different levels for the factors based on the three existing Bayesian implementations. Full factorial experiments are then conducted on the specified factors both for real computer models and via simulation with the aim of identifying the significant factors. Emphasis is placed on the prediction accuracy, since the performances of the prediction coverage probability for most combinations are satisfactory. Through the analyses described above, we find that among the four factors, two factors are actually significant to the prediction accuracy. The best combination for the levels of the four factors is also identified. === Science, Faculty of === Statistics, Department of === Graduate
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