Latin Hypercube Sampling

Latin Hypercube Sampling (LHS) is a statistical sampling technique widely used in experimental design and sensitivity analysis. It ensures balanced representation of each input variable across its entire distribution range by dividing the cumulative distribution into equally probable intervals and selecting one sample from each interval. This approach effectively reduces variability in output responses and enhances Monte Carlo simulation efficiency. Implementation typically involves two primary methodologies: basic sampling for independent variables and correlated sampling for dependent variables using techniques like Cholesky decomposition or covariance matrix transformation. Additional critical steps include variable importance ranking through sensitivity indices, optimal sample size determination via convergence analysis, and evaluation/validation of sampling schemes using goodness-of-fit tests. Algorithmically, LHS can be implemented through stratification and permutation operations, with key functions involving random permutation generation and interval-based sample allocation. Widely adopted in engineering and computational science, LHS maximizes information extraction from minimal samples while maintaining probabilistic representativeness, making it particularly valuable for resource-intensive simulations.