拉丁超立方抽樣
外觀
![](http://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/LHSsampling.png/220px-LHSsampling.png)
拉丁超立方抽樣(英語:Latin hypercube sampling,縮寫LHS)是一種從多元參數分佈中近似隨機抽樣的方法,屬於分層抽樣技術,常用於計算機實驗或蒙特卡洛積分等。
麥凱(McKay)等人於1979年提出了拉丁超立方抽樣。[1]不過此前Eglājs於1977年獨立提出過相同的抽樣技術。[2]1981年,伊曼(Ronald L. Iman)等進一步發展了該方法。[3]
在統計抽樣中,拉丁方陣是指每行、每列僅包含一個樣本的方陣。拉丁超立方則是拉丁方陣在多維中的推廣,每個與軸垂直的超平面最多含有一個樣本。
假設有個變量(維度),可以將每個變量分為個概率相同的區間。此時,可以選取個滿足拉丁超立方條件的樣本點。需要注意的是,拉丁超立方抽樣要求每個變量的分區數量相同。不過,該方法並不要求當變量增加時樣本數同樣增加。
參考文獻
[編輯]- ^ McKay, M.D.; Beckman, R.J.; Conover, W.J. A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (JSTOR Abstract). Technometrics (American Statistical Association). May 1979, 21 (2): 239–245. ISSN 0040-1706. JSTOR 1268522. OSTI 5236110. doi:10.2307/1268522.
- ^ Eglajs, V.; Audze P. New approach to the design of multifactor experiments. Problems of Dynamics and Strengths. 35 (Riga: Zinatne Publishing House). 1977: 104–107 (俄語).
- ^ Iman, R.L.; Helton, J.C.; Campbell, J.E. An approach to sensitivity analysis of computer models, Part 1. Introduction, input variable selection and preliminary variable assessment. Journal of Quality Technology. 1981, 13 (3): 174–183.
延伸閱讀
[編輯]- Tang, B. Orthogonal Array-Based Latin Hypercubes. Journal of the American Statistical Association. 1993, 88 (424): 1392–1397. JSTOR 2291282. doi:10.2307/2291282.
- Owen, A.B. Orthogonal arrays for computer experiments, integration and visualization. Statistica Sinica. 1992, 2: 439–452.
- Ye, K.Q. Orthogonal column Latin hypercubes and their application in computer experiments. Journal of the American Statistical Association. 1998, 93 (444): 1430–1439. JSTOR 2670057. doi:10.2307/2670057.
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