高斯隨機域模型下的效應混淆

部分因子實驗在科學界與業界的研發常被使用，而使用部分因子設計必然會使得因子效應之間產生混淆。在文獻上，效應混淆的議題在貝氏設計與電腦實驗中常使用的高斯隨機域模型下並未受到探討。此論文提出一高斯隨機域的線性結構，並在此結構下，分別對質性因子與量性因子探討高斯隨機域模型中效應混淆的議題。我們建立了高斯隨機域中效應的概念，並提出一衡量效應混淆嚴重程度的指標。此指標除了可呈現效應混淆的資訊外，亦涵蓋了模型複雜度的概念。我們也探討了效應混淆對模型一些統計性質上的影響，像是參數估計、效應的貝氏後驗共變異數矩陣以及預測變異數。

關鍵字

部分因子設計；貝氏設計；電腦實驗；克利金模型

並列摘要

Effect aliasing is an inevitable consequence of using fractional factorial designs. For Gaussian random field models, advocated in some Bayesian design and computer experiment literature, the impact of effect aliasing has not received adequate attention. In this dissertation, we establish a kind of linear model structure to define effects for a Gaussian random field, and study effect aliasing in Gaussian random field models under fractional factorial designs with qualitative and with quantitative factors individually. An aliasing severity index is proposed to assess the severity level of aliasing, for which the notion of priority order and model complexity is established. Some impacts of aliasing on parameter estimation, posterior variances of effects under a Bayesian framework, and prediction variance are addressed as well.

並列關鍵字

Fractional factorials ； Bayesian design ； computer experiments ； kriging

參考文獻

Adler, R. J. and Taylor, J. E. (2007), Random Fields and Geometry, Springer.

Ai, M. Y., Li, P. F., and Zhang, R. R. (2005), “Optimal criteria and equivalence for nonregular fractional factorial designs”, Metrika, 72–83.

Cheng, C. S., Deng, L. Y., and Tang, B. (2002), “Generalized minimum aberra- tion and design efficiency for nonregular fractional factorial designs”, Statistica Sinica, 12, 991–1000.

Cheng, C. S., Steinberg, D. M., and Sun, D. X. (1999), “Minimum aberration and model robustness for two-level fractional factorial designs”, J. R. Statist. Soc. Ser. B, 61, 85–93.

Cheng, S. W. and Ye, K. Q. (2004), “Geometric isomorphism and minimum aber- ration for factorial designs with quantitative factors”, Annals of Statistics, 32, 2168–2185.

國際替代計量

高斯隨機域模型下的效應混淆

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