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''A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code'', in ''Technometrics 21: 239-245''.
In the context of statistical sampling, a square grid containing sample positions is a [[Latin square]] if (and only if) there is only one sample in each row and each column. A '''Latin hypercube''' is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned hyperplane containing it.
When sampling a function of <math>N</math> variables, the range of each variable is divided into <math>M</math> equally probable intervals. <math>M</math> sample points are then placed to satisfy the Latin hypercube requirements; note that this forces the number of divisions, <math>M</math>, to be equal for each variable. Also note that this sampling scheme does not require more samples for more dimensions (variables); this independence is one of the main advantages of this sampling scheme. Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far.
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[[Category:Statistics]]
[[Category:Latin squares]]
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