Overview
Latin hypercube sampling improves coverage over independent random sampling by stratifying each dimension independently.
CoreSource checked
Latin Hypercube Sampling
Samples each dimension so every interval stratum is used exactly once.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Randomness & Sampling
- Difficulty
- Intermediate
- Family
- Stratified Sampling
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 1
- Relationships
- 3
- Code example
- Ready
- Visualization
- Ready
Core Concepts
dimension stratificationpermutationsample coveragevariance reduction
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n d)
Average
O(n d)
Worst
O(n d)
Space
O(n d)
When to Use
- Use when monte Carlo simulation needs dimension stratification.
- Use when the input matches the assumptions behind stratified Sampling.
When Not to Use
- Avoid when independence, reproducibility, or distribution quality cannot be checked.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Samples each dimension so every interval stratum is used exactly once
- Uses dimension stratification and permutation to guide the work.
- Produces samples.
Use Cases
- Monte Carlo simulation
- Randomized algorithms
- Sampling distributions
Inputs
- Random source
- Distribution or weights
- Sample count
Outputs
- Samples
- Estimated statistic
- Randomized selection
Key Formulas (1)
Stratum sample
x = (perm[i] + u) / N
x = (perm[i] + u) / NPlaces one random point inside each dimension's assigned stratum.
Pseudocode
- 1.Initialize the random source, sequence state, or sampler parameters
- 2.Generate the next candidate, variate, or structured random choice
- 3.Accept, transform, weight, or record the value according to the method
- 4.Repeat until the requested sample count or stopping rule is reached
Canonical Example
- Input
- seed = 7, sample count = 5, and a small target distribution or domain
- Output
- Samples
- Explanation
- Latin Hypercube Sampling applies dimension stratification to produce samples.
Implementation Notes
- Expose seed handling when reproducibility is important.
- Keep the dimension stratification step separate enough to test independently.
- Separate the random source from the sampler so tests can use fixed seeds and distribution checks.
Common Pitfalls
- Using a biased random source can quietly invalidate downstream estimates.
- Test edge cases, not only clean examples.
- Uncontrolled seeds or biased random choices can make results irreproducible or statistically misleading.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryPlot generated samples against the target distribution or domain.
Step 1 of 4: Initialize the random source, sequence state, or sampler parameters
randomness-sampling-mechanismNotes
Latin Hypercube Sampling should be used with the assumptions and tradeoffs of stratified Sampling in mind.
Sources (2)
What each reference supports for this entry.
Latin Hypercube Sampling
PaperOriginal reference for Latin hypercube sampling in computer experiments.
Open sourceMonte Carlo Statistical Methods
BookMonte Carlo reference for Latin Hypercube Sampling's estimator construction, sampling assumptions, and variance behavior.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toSobol Sequence
Both improve multidimensional coverage with different deterministic or randomized designs.
Variant ofStratified Sampling
Latin Hypercube Sampling stratifies each dimension of the sample space.
Related Algorithms
Tags
Randomness & SamplingStratified SamplingSamplingStochastic