The statistical method Latin hypercube sampling was developed and invented by Ronald L. Iman, J. C. Helton, and J. E. Campbell, et al to generate a distribution of plausible collections of parameter values from a multidimensional distribution.
Their paper An approach to sensitivity analysis of computer models, Part I. Introduction, input variable selection and preliminary variable assessment. appeared in the Journal of Quality Technology in 1981.
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 variables, the range of each variable is divided into different regions. sample points are then placed to satisfy the Latin hypercube requirements; note that this forces the number of divisions, , 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.
