Latin Hypercube Sampling — Stratified Simulation Design
Latin Hypercube Sampling and Sensitivity Analysis · Also known as: LHS, Latin Hiperküp Örnekleme (LHS) ve Duyarlılık Analizi, stratified sampling design, space-filling design
Latin Hypercube Sampling (LHS) is a stratified space-filling design for computer experiments, introduced by McKay, Beckman, and Conover in 1979. It divides each input variable's range into equally probable strata and draws exactly one sample per stratum, ensuring that the full input space is covered with far fewer model evaluations than standard Monte Carlo simulation requires. It is routinely paired with global sensitivity analysis — particularly Sobol indices — to quantify how much each input drives output variability.
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When to use it
LHS is appropriate whenever you need to explore how a computationally expensive model responds across its input space and a full factorial or random Monte Carlo design would be prohibitively costly. The method requires that input variable bounds and distributions can be specified — even approximate marginal distributions are sufficient. It is particularly well-suited for global sensitivity analysis when inputs are continuous. If inputs are strongly correlated, apply the Iman-Conover correction before sampling. When the model is very cheap to evaluate, standard Monte Carlo with a very large sample size is a simpler alternative; when you need only local sensitivity, gradient-based methods may be more informative.
Strengths & limitations
- Achieves similar estimation accuracy to standard Monte Carlo with substantially fewer model evaluations, making it highly efficient for expensive simulations.
- Guarantees full coverage of each input variable's range through stratification, eliminating the clustering and gaps that plague pure random sampling.
- Pairs naturally with Sobol global sensitivity indices, enabling a principled ranking of input importance.
- Applicable to any black-box model — no derivative information or analytic form is required.
- The Iman-Conover extension handles correlated inputs without sacrificing the space-filling property.
- Requires that input distributions and bounds be specified in advance; poorly chosen distributions can misrepresent the true parameter space.
- Sobol sensitivity analysis demands a sample size of N·(k+2), which can become large when the number of inputs k is high.
- LHS does not guarantee optimality in high-dimensional spaces — the advantage over random sampling diminishes as dimensionality grows.
- The method is purely exploratory; it does not itself estimate uncertainty of the output distribution without additional analysis.
Frequently asked
How is LHS different from standard Monte Carlo sampling?
Both methods are used to sample an input space for simulation, but they differ in how they place samples. Standard Monte Carlo draws each sample point independently and uniformly at random, which can leave some regions of the input space over-represented and others sparse purely by chance. LHS enforces a stratification rule: each input variable's range is divided into equally probable intervals, and exactly one sample is placed in each interval. This guarantees better coverage of the input space with the same number of points, leading to lower estimation variance for many quantities of interest.
How many samples are needed?
A minimum of 1000 sample points is the commonly recommended threshold for reliable coverage of the input space with LHS. For Sobol sensitivity analysis the required sample size is N·(k+2), where k is the number of input variables. For example, with 10 inputs and N = 1024, the total number of model evaluations is 12 288. Below 1000 samples, the space-filling advantage of LHS narrows and Sobol indices become highly uncertain.
What are Sobol indices and why are they used with LHS?
Sobol indices are variance-based sensitivity measures. The first-order index S_i quantifies how much of the total output variance is explained by input i alone; the total-order index S_Ti captures the combined effect of input i and all its interactions with other inputs. They are commonly paired with LHS because LHS produces a well-spread sample over the input space, which is the starting point for the Saltelli estimator of Sobol indices. Together, the two techniques identify which inputs drive model output and which can be treated as fixed — a key step in model simplification and calibration planning.
What should I do when inputs are correlated?
Standard LHS generates samples under the assumption that inputs are independent. When inputs are correlated, apply the Iman-Conover rank-correlation method as a post-processing step: it rearranges the LHS columns to induce the desired rank correlations among inputs while preserving the marginal distributions and the stratification property. Ignoring known correlations inflates or deflates sensitivity estimates and gives a misleading picture of which inputs matter most.
Sources
- McKay, M.D., Beckman, R.J. & Conover, W.J. (1979). 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. DOI: 10.1080/00401706.1979.10489755 ↗
- Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M. & Tarantola, S. (2008). Global Sensitivity Analysis: The Primer. Wiley. DOI: 10.1002/9780470725184 ↗
How to cite this page
ScholarGate. (2026, June 1). Latin Hypercube Sampling and Sensitivity Analysis. ScholarGate. https://scholargate.app/en/simulation/latin-hypercube-sampling
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