查看“︁拉丁超立方抽样”︁的源代码

[[File:LHSsampling.png|thumb|right|图中II为拉丁超立方抽样的示意图。I和III则分别为随机抽样与正交抽样的示意图。]]
'''拉丁超立方抽样'''（{{lang-en|Latin hypercube sampling}}，缩写{{lang|en|LHS}}）是一种从多元参数分布中近似随机[[抽样]]的方法，属于[[分层抽样]]技术，常用于计算机实验或蒙特卡洛积分等。

麦凯（McKay）等人于1979年提出了拉丁超立方抽样。<ref name = "C3M">{{cite journal
| last        = McKay
| first       = M.D. |author2=Beckman, R.J. |author3=Conover, W.J.
|date=May 1979
| title       = A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
| url        = https://archive.org/details/sim_technometrics_1979-05_21_2/page/239
| journal     = Technometrics
| volume      = 21
| issue       = 2
| pages       = 239–245
| publisher   = American Statistical Association
| issn        = 0040-1706
| doi         = 10.2307/1268522
| format      = JSTOR Abstract
| laysummary  = 
| laysource   = 
| laydate     = 
| quote=
| osti        = 5236110
| jstor         = 1268522
}}
</ref>不过此前Eglājs于1977年独立提出过相同的抽样技术。<ref>{{cite journal|last=Eglajs|first=V.|author2=Audze P. |title=New approach to the design of multifactor experiments|journal=Problems of Dynamics and Strengths|year=1977|series=35|pages=104–107|publisher=Zinatne Publishing House|location=Riga|language=ru}}</ref>1981年，伊曼（Ronald L. Iman）等进一步发展了该方法。<ref>{{cite journal |last=Iman |first=R.L. |author2=Helton, J.C. |author3=Campbell, J.E.|title=An approach to sensitivity analysis of computer models, Part 1. Introduction, input variable selection and preliminary variable assessment |url=https://archive.org/details/sim_journal-of-quality-technology_1981-07_13_3/page/174 |journal=Journal of Quality Technology |volume=13 |issue=3 |pages=174–183  |year=1981 }}</ref>

在统计抽样中，[[拉丁方阵]]是指每行、每列仅包含一个样本的方阵。'''拉丁超立方'''则是拉丁方阵在多维中的推广，每个与轴垂直的[[超平面]]最多含有一个样本。

假设有<math>N</math>个变量（维度），可以将每个变量分为<math>M</math>个概率相同的区间。此时，可以选取<math>M</math>个满足拉丁超立方条件的样本点。需要注意的是，拉丁超立方抽样要求每个变量的分区数量<math>M</math>相同。不过，该方法并不要求当变量增加时样本数<math>M</math>同样增加。

== 参考文献 ==
{{reflist}}

== 延伸阅读 ==
*{{cite journal |doi=10.2307/2291282 |last=Tang |first=B. |title=Orthogonal Array-Based Latin Hypercubes |url=https://archive.org/details/sim_journal-of-the-american-statistical-association_1993-12_88_424/page/1392 |journal=Journal of the American Statistical Association |volume=88 |issue=424 |pages=1392–1397  |year=1993 |jstor=2291282 }}
*{{cite journal |last=Owen |first=A.B. |title=Orthogonal arrays for computer experiments, integration and visualization |journal=Statistica Sinica |volume=2 |pages=439–452  |year=1992 }}
*{{cite journal |doi=10.2307/2670057 |last=Ye |first=K.Q. |title=Orthogonal column Latin hypercubes and their application in computer experiments |url=https://archive.org/details/sim_journal-of-the-american-statistical-association_1998-12_93_444/page/1430 |journal=Journal of the American Statistical Association |volume=93 |issue=444 |pages=1430–1439  |year=1998 |jstor=2670057 }}

{{Experimental design}}
{{统计学}}

[[Category:实验设计]]
[[Category:统计方法]]