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研究生:魏郁錡
研究生(外文):Yu-Chi Wei
論文名稱(外文):Optimal Multi-platform Designs Based on Two Statistical Approaches
指導教授:張明中張明中引用關係
指導教授(外文):Ming-Chung Chang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2019
畢業學年度:107
語文別:英文
論文頁數:60
中文關鍵詞:最佳化設計
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在線試驗或是多變量實驗是一種在網路世界快速成長的方法,在網路世界用於各種應用上,像是網站或是郵件的最佳化。隨著科技快速成長,在線測試常常使用在許多平台上,像是筆記型電腦、智慧型手機與智慧型手錶。因此設計在多個平台上有效的在線測試是非常緊迫的問題。Sadeghi et al. (2016) 與 Sadeghi et al.(2017) 分別對於兩個水準與四個水準的多平台實驗提出挑選設計的準則。然而,這種修改的準則缺乏強力的統計理由。在這篇論文中,我們通過兩種方法研究這樣的設計問題,稱為貝氏方法與泰勒級數方法。我們也針對各種因子個數以及水準組合個數提供了使用我們方法找出來的最佳設計。
Online testing or multivariate experiment is a method that grows rapidly
in the digital world for various applications, such as website and email
optimization. Due to the highly development of technology, online testings are more often conducted on other platforms, such as laptops, smartphones, and smart watches. Thus, designing efficient online testings across
multiple platforms is an urgent issue. Sadeghi et al. (2016) proposed
a design selection criterion for two-level multiple-platform experiments.
Sadeghi et al. (2017) further extended Sadeghi et al. (2016) to fourlevel factors. However, such naive modifications lack strong statistical justifications. In this thesis, we study such design problem through two approaches, referred to as Bayesian method and Taylor Series method. We
also provide optimal designs based on our methods for various run sizes and
numbers of factors.
Contents
List of Tables iv
List of Figures vi
1 Introduction 1
2 Literature Review 2
2.1 Fractional Factorial Designs . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Optimal two-level Design . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Optimal four-level Design . . . . . . . . . . . . . . . . . . . . . . . 6
3 Bayesian Approach Method 7
3.1 Prior Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Optimal Design with one two-level Sliced factor S . . . . . . . . . . 10
3.3 Optimal Design for the four-level Sliced factor S . . . . . . . . . . . 13
4 Taylor Series Method 17
4.1 Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 Optimal two-level Design . . . . . . . . . . . . . . . . . . . . . . . . 19
4.3 Optimal four-level Design . . . . . . . . . . . . . . . . . . . . . . . 22
5 A Swarm Intelligence Based Method 24
5.1 Review Particle Swarm Optimization . . . . . . . . . . . . . . . . . 24
5.2 Swarm Intelligence Based algorithm . . . . . . . . . . . . . . . . . . 25
5.3 MIX operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.4 MOVE operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6 Example 27
7 Conclusion 30
References 48
References
[1] Sadeghi, S., Qian, P. Z. G., and Arora, N. ”Sliced designs for multi-platform
online experiments.” (2016).
[2] Sadeghi, S., Qian, P. Z. G., and Arora, N. ”Sliced minimum aberration designs
for four-platform experiments.” (2017).
[3] Fries, A., and Hunter, W. G. ”Minimum aberration 2 k–p designs.” Technometrics 22.4 (1980): 601-608.
[4] Joseph, V. R. ”A Bayesian approach to the design and analysis of fractionated
experiments.” Technometrics 48.2 (2006): 219-229.
[5] Kang, L., and Joseph, V. R. ”Bayesian optimal single arrays for robust parameter design.” Technometrics 51.3 (2009): 250-261.
[6] Joseph, V. R., and Delaney, J. D. ”Functionally induced priors for the analysis
of experiments.” Technometrics 49.1 (2007): 1-11.
[7] Wu, C. F. J., and Hamada, M. S. Experiments: planning, analysis, and
optimization. Vol. 552. John Wiley Sons, 2011.
[8] Phoa, F. K. H. ”A Swarm Intelligence Based (SIB) method for optimization
in designs of experiments.” Natural Computing 16.4 (2017): 597-605.
[9] Eberhart, R., and Kennedy, J. ”A new optimizer using particle swarm theory.” MHS’95. Proceedings of the Sixth International Symposium on Micro
Machine and Human Science. IEEE, 1995.
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