Latin Hypercube Sampling

Application Context When employing Latin Hypercube Sampling (LHS) to sample from multiple variables, maintaining independence between variables is crucial. Values sampled for one variable must be independent of those sampled for other variables (unless intentional correlation is desired). Independence preservation is achieved by randomly selecting sampling intervals for each variable. In a given iteration, variable #1 may sample from stratum #4 while variable #2 samples from stratum #22, ensuring both randomness and independence while preventing unintended correlations. As a more efficient sampling technique, LHS offers significant benefits in sampling efficiency and runtime performance (due to fewer iterations). These advantages are particularly notable in PC-based simulation environments like @RISK.

Sample Creation with Latin Hypercube Sampling and Spatial Correlation Using Cholesky Decomposition Algorithm

This source code generates random fields over a square spatial domain. The implementation combines Latin Hypercube Sampling for sample generation with spatial correlation modeling through the Cholesky decomposition algorithm, ensuring both uniform point distribution and accurate correlation structure in the resulting random field.