Latin Hypercube Sampling

TLDR: Latin hypercube sampling (LHS) as mentioned in this paper uses a stratified sampling scheme to improve on the coverage of the k-dimensional input space for such computer models, which is more efficient than simple random sampling in a large range of conditions.

Abstract: This entry discusses the use of computer models for such diverse applications as safety assessments for geologic isolation of radioactive waste and for nuclear power plants; loss cost projections for hurricanes; reliability analyses for manufacturing equipment; transmission of HIV; and subsurface storm flow modelling. Such models are usually characterized by a large number of input variables (perhaps as many as a few hundred), and usually, only a handful of these inputs are important for a given response. In addition, the model response is frequently multivariate and time dependent. Latin hypercube sampling (LHS) uses a stratified sampling scheme to improve on the coverage of the k-dimensional input space for such computer models. This means that a single sample will provide useful information when some input variable(s) dominate certain responses (or certain time intervals), while other input variables dominate other responses (or time intervals). By sampling over the entire range, each variable has the opportunity to show up as important, if it indeed is important. If an input variable is not important, then the method of sampling is of little or no concern. The values of the stratified sampling scheme can be paired to ensure a desired correlation structure among the k input variables. LHS is more efficient than simple random sampling in a large range of conditions. Keywords: Latin hypercube sampling; uncertainty analysis; sensitivity analysis; rank correlation; hurricane loss projection; uncertainty importance