在過去的近幾十年來，電腦實驗受到了廣泛的關注，並在解決不同的科學和工程問題中發揮著越來越重要的作用。而在電腦實驗的領域中，高斯過程是一個最常被使用的模型。因此，本論文主要是研究在高斯過程模型下的變數篩選問題。為了降低計算成本，本論文採用梯度方法而不是貝葉斯方法來構建變數篩選的演算法。此外，為了同時考慮高斯過程模型的均值函數和相關函數，本論文也提出了幾種梯度選擇方法來標準化模型的兩種類型的梯度值。因此，在此基礎上，本論文提出了兩種變數篩選演算法，分別是向前篩選程序 (Forward Screening Procedure) 和批量向後篩選程序 (Batchwise Backward Screening Procedure)。最後，使用兩種不同的模擬研究來說明所提出方法的性能。

In recent decades, computer experiments have received widespread attention from all over the world, and have played an increasingly important role in solving different sciences and engineering. In this thesis, we are interested in the variable screening problems for Gaussian process models in computer experiments. However, to reduce the computational cost, we adopt the gradient approach instead of the Bayesian approach to construct our variable screening algorithm. In addition, to consider the mean function and the correlation function of the Gaussian process model simultaneously, we propose several gradient selection methods to standardize the two types of gradient values. Therefore, we propose two variable screening algorithms, namely the Forward Screening Procedure (FSP) and the Batchwise Backward Screening Procedure (BBSP). Lastly, two different simulation studies are used to illustrate the performance of the proposed approaches.

Andrianakis, I., & Challenor, P. G. (2012). The effect of the nugget on gaussian process emulators of computer models. Computational Statistics & Data Analysis, 56(12), 4215–4228.

Dellaportas, P., Forster, J. J., & Ntzoufras, I. (2002). On bayesian model and variable selection using mcmc. Statistics and Computing, 12(1), 27–36.

Eberhart, R., & Kennedy, J. (1995). Particle swarm optimization. In Proceedings of the ieee international conference on neural networks (Vol. 4, pp. 1942–1948).

Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American statistical Association, 96(456), 1348–1360.

Forrester, A., Sobester, A., & Keane, A. (2008). Engineering design via surrogate modelling: a practical guide. John Wiley & Sons.

George, E. I., & McCulloch, R. E. (1993). Variable selection via gibbs sampling. Journal of the American Statistical Association, 88(423), 881–889.

Guyon, I., & Elisseeff, A. (2003). An introduction to variable and feature selection. Journal of machine learning research, 3(Mar), 1157–1182.

Hocking, R. R. (1976). A biometrics invited paper. the analysis and selection of variables in linear regression. Biometrics, 1–49.

Huang, H., Lin, D. K., Liu, M.-Q., & Zhang, Q. (2020). Variable selection for kriging in computer experiments. Journal of Quality Technology, 52(1), 40–53.

Lee, K.-J., Chen, R.-B., & Wu, Y. N. (2016). Bayesian variable selection for finite mixture model of linear regressions. Computational Statistics & Data Analysis, 95, 1–16.

Linkletter, C., Bingham, D., Hengartner, N., Higdon, D., & Ye, K. Q. (2006). Variable selection for gaussian process models in computer experiments. Technometrics, 48(4), 478–490.

Sacks, J., Schiller, S. B., & Welch, W. J. (1989). Designs for computer experiments. Technometrics, 31(1), 41–47.

Sacks, J., Welch, W. J., Mitchell, T. J., & Wynn, H. P. (1989). Design and analysis of
computer experiments. Statistical science, 409–423.

Singh, S., Kubica, J., Larsen, S., & Sorokina, D. (2009). Parallel large scale feature selection for logistic regression. In Proceedings of the 2009 siam international conference on data mining (pp. 1172–1183).

Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267–288.

Zhang, F. (2018). Bayesian indicator variable selection in gaussian process for computer experiments (Unpublished master's thesis). National Cheng Kung University, Tainan.

Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American statistical association, 101(476), 1418–1429.