Latin hypercube sampling: Difference between revisions

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The [[statistics|statistical]] method of '''Latin hypercube sampling''' ('''LHS''') was developed to generate a distribution of plausible collections of parameter values from a [[multidimensional distribution]]. The [[Sampling (statistics)|sampling method]] is often applied in [[uncertainty]] analysis.

The technique was first described by McKay<ref>{{cite journal |last=McKay |first=M.D. |coauthors=Conover, W.J.; and Beckman, R.J. |title=A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code |year=1979 |journal=Technometrics |volume=21 |pages=239–245}}</ref> in [[1979]]. It was furherfurther elaborated by [[Ronald L. Iman]], and others<ref>{{cite journal |last=Iman |first=R.L. |coauthors=Helton, J.C.; and [[James Edward Campbell|Campbell, J.E.]] |title=An approach to sensitivity analysis of computer models, Part 1. Introduction, input variable selection and preliminary variable assessment |journal=Journal of Quality Technology |volume=13 |issue=3 |pages=174–183 |year=1981 }}</ref> in [[1981]]. Detailed computer codes and manuals were later published.<ref>{{cite book |last=Iman |first=R.L. |coauthors=Davenport, J.M. ; Zeigler, D.K. |title=Latin hypercube sampling (program user's guide) |year=1980 |id={{OSTI|5571631}}}}</ref>

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.