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研究生： 林冠瑤
Kuan-Yao Lin
論文名稱： Study on the Prediction Capability of Two Aliasing Indices for Gaussian Random Fields
指導教授： 張明中
Ming-Chung Chang
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
論文出版年： 2020
畢業學年度： 108
語文別： 英文
論文頁數： 47
中文關鍵詞： 部分因子設計 、電腦實驗
外文關鍵詞： fractional factorial design, computer experiment
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    • 部分因子設計會造成因子效應混淆，導致難以掌握因子與反應變數之間的關係。在高斯隨機域的模型假設下，Chang et al.（2018）和 Chang and Cheng（2020）提出了兩個衡量因子效應混淆的指標，分別用來評估類別型因子與連續型因子的效應混淆之嚴重程度，然而這兩個指標與統計性質之間的連結仍然不清楚。在本篇論文中，我們展示了此二指標與因子設計之預測能力有高度相關，並利用數值模擬來觀察低程度混淆的因子設計與預測偏誤和預測變異之關聯。

    The existence of effect aliasing in fractional factorial designs makes it difficult to accurately understand the relationship between the factors and the response. For Gaussian random fields, two indices for assessing the degree of severity of effect aliasing have been proposed by Chang et al. (2018) and Chang and Cheng (2020), the former for qualitative factors and the latter for quantitative factors. However, the connection between these two indices and statistical properties remained vague. In this thesis, we show that the two aliasing severity indices are highly correlated with prediction performance of fractional factorial designs. We conduct simulation study to evaluate low-aliasing designs through their prediction bias and prediction variance over the whole experimental region.

    Contents 摘要 i Abstract ii 誌謝 iii Contents iv List of figures vi 1 Introduction 1 2 Literature Review 3 3 Comparing qualitative signal aliasing index with different criteria 6 3.1 Average prediction variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Mean square error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4 Comparing quantitative signal aliasing index with different criteria 25 4.1 Average prediction variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 Mean square error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5 Conclusion 33 Appendix 34 References 35 iv

    References
    CHANG, M. C., CHENG, S. W., AND CHENG, C. S. (2018). Signal aliasing in Gaussian
    random fields for experiments with qualitative factors. Ann. Statist., 47(2), 909-935.
    CHANG, M. C. AND CHENG, S. W. (2020). Effect aliasing in Gaussian random fields with
    quantitative treatment factors. manuscript.
    KERR, M. K. (2001). Bayesian optimal fractional factorials. Statist. Sinica, 11, 605-630.
    LEVY, S. AND STEINBERG, D. M. (2010). Computer experiments: a review. AStA., 94,
    311-324.
    PLUMLEE, M. AND JOSEPH, V. R. (2018). Orthogonal Gaussian process models. Statist.
    Sinica, 28, 601-619.
    STEINBERG, D. M. AND BURSZTYN, D. (2004). Data analytic tools for understanding
    random field regression models. Technometrics, 46(4), 411-420.
    WU, C. F. J. AND HAMADA, M. S. (2009). Experiments: Planning, Analysis, and Optimization, 2nd ed. . Wiley, Hoboken, NJ. MR2583259
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