Study on the Prediction Capability of Two Aliasing Indices for Gaussian Random Fields

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林冠瑤(Kuan-Yao Lin) 查詢紙本館藏

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統計研究所

論文名稱

(Study on the Prediction Capability of Two Aliasing Indices for Gaussian Random Fields)

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至系統瀏覽論文 (2025-6-30以後開放)

摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 部分因子設計
★ 電腦實驗

關鍵字(英)

★ fractional factorial design
★ computer experiment

論文目次

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

參考文獻

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
35

指導教授

張明中(Ming-Chung Chang)

審核日期

2020-7-14

推文