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Monte Carlo Analysis
Model-Based Monte Carlo Simulation
where f H depends only on the horizontal variable, f V depends only on the vertical one, and the
residual f RES is defined by subtraction.
Latin hypercube sampling will give an error that is largely unaffected by the additive part
f H (u) +f V (u). One can prove that the variance in Latin hypercube sampling is approximately
σ 2 RES /n where σ RES is the smallest variance of f RES for any decomposition of f.
LHS versus Random
The LHS method ensures that each of these components is represented in a fully stratified
manner, no matter which components might turn out to be important. It can be proved that LHS
is never worse than random sampling for estimating the mean and the population distribution
function. In particular the closer the output function is to being additive in its input variables,
the more reduction in variance (variance of the mean estimator).
When choosing the Monte Carlo sampling plan best suited for your analysis, follow these
guidelines:
• For uncertainty and sensitivity analyses, choose the standard Monte Carlo sampling plan
(RAND).
• For Large Scale Sensitivity (LSS) analysis, it makes sense to choose the Latin
Hypercube Sampling (LHS) method. It is related to the stratification method used in this
approach. The disadvantage of this method is the lack of a save/restart feature; the
current samples cannot be augmented with additional points. The LHS plans are in some
way very monolithic, unlike the standard Monte Carlo sampling plan which is very
flexible.
The LHS method is based on the classical approach, the stratification method used in LHS takes
into account the underlying distribution. The LHS sampling is uniform, (0, 1) N , but the resulting
sample is obtained by transforming this uniform sample into the scales (and shape) of the joint
probability distribution.
Related Topics
Sampling Plan Methods
Model-Based Monte Carlo Simulation
The basic idea of a model-based Monte Carlo simulation is to perform surrogate modeling to
drastically reduce the number of simulations from the response function of interest. The
surrogate model serves as a substitute for the high-fidelity SPICE simulations in the context of
Monte Carlo analysis.
The name that we used in Eldo to denote this feature is “Super Saturated Design” (SSD). It
refers to the early developments of the approach for constructing design plans satisfying optimal
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