Applies to: @RISK and RISKOptimizer

Difference Between Monte Carlo and Latin Hypercube Sampling

The @RISK and RISKOptimizer manuals state:
"We recommend using Latin Hypercube, the default sampling type setting, unless your modeling situation specifically calls for Monte Carlo sampling."

Here’s what that means:

Monte Carlo Sampling

• Traditional technique using random or pseudo-random numbers to sample from a probability distribution.

• Any given sample can fall anywhere within the range of the distribution.

• With enough iterations, Monte Carlo recreates the input distribution, but clustering can occur with a small number of iterations.

• The Central Limit Theorem (CLT) applies: the sample mean is expected to fall within the standard error of the distribution mean.

Example:

• Input: RiskNormal(655,20)

• Iterations: 100

• Standard error of the mean (SEM): 20 / √100 = 2

• ~68% of sample means should fall within ±1 SEM, ~95% within ±2 SEM.

Latin Hypercube Sampling

• Stratified sampling: divides the cumulative probability distribution into equal intervals, taking a random value from each interval.

• Number of intervals = number of iterations.

• Not purely random; the CLT does not apply.

• Ensures that all or nearly all sample means fall close to the true distribution mean, even with modest iteration counts.

• Multiple simulations converge faster because means across simulations are much closer than with Monte Carlo.

Key point: With Latin Hypercube, even a single simulation closely approximates the input distribution, which is especially useful for smaller iteration counts.

Comparison

• Uniform distributions or discrete integers make differences visible.

• In testing with 720 iterations and various distributions, Latin Hypercube consistently produced means that were much closer together than Monte Carlo.

• Artificial or real-world scenarios show that Latin Hypercube reduces variability in sample means and improves convergence.

Recommendations

Default: Latin Hypercube

Use Monte Carlo only if your modeling situation specifically requires purely random sampling.

 

Related Articles:

Confidence Intervals in @RISK

How Many Iterations Do I Need?

Attachments:
KB0028_StandardErrorLHandMC_61orOlder.xls
KB0028_A_MonteCarlo.xlsx
KB0028_B_LatinHypercube.xlsx
KB0028_StandardErrorLHandMC_62or63.xlsm
KB0028_StandardErrorLHandMC_7x.xlsm