Latin Hypercube¶
Above is an example of a Latin Hypercube design for \(k = 2\) factors and \(n = 7\) runs (levels).
Latin Hypercube designs are model independent, space filling designs often used in computer experiments. In these designs each of the \(k\) factors is divided into \(n\) equal levels such that there is only one run containing a given level of a factor. The number of total runs is also equal to \(n\).
Presently these designs are optimized by distance in order fill out the factor space. The integer levels are converted to the -1 to +1 coded space and subsequently the space of actual factor values.
Numeric Factors: The number of continuous numeric factors in the Latin hypercube design.
Runs: The number of runs \(n\) in the design and the number of levels for each numeric factor.
References
Brian Beachkofski and Ramana Grandhi. Improved Distributed Hypercube Sampling, pages 1–7. Number 1274. American Institute of Aeronautics and Astronautics, 2002.
M.D. McKay, R.J. Beckman, and W.J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2):239–245, 1979.
Michael Stein. Large sample properties of simulations using latin hypercube sampling. Technometrics, 29(2):143–151, 1987.