Latin Hypercube Sampling

In Latin Hypercube sampling, Crystal Ball divides each assumption’s probability distribution into  nonoverlapping segments, each having equal probability, as illustrated below (Figure 7, Normal Distribution with Latin Hypercube Sampling Segments).

Figure 7. Normal Distribution with Latin Hypercube Sampling Segments

This image is a segmented curve that is highest in the middle and tapers down evenly on both sides.

While a simulation runs, Crystal Ball selects a random assumption value for each segment according to the segment’s probability distribution. This collection of values forms the Latin Hypercube sample. After Crystal Ball has sampled each segment exactly once, the process repeats until the simulation stops.

The Sample Size option (displayed when you select Run Preferences, then Sample), controls the number of segments in the sample.

Latin Hypercube sampling is generally more precise when calculating simulation statistics than is conventional Monte Carlo sampling, because the entire range of the distribution is sampled more evenly and consistently. Latin Hypercube sampling requires fewer trials to achieve the same level of statistical accuracy as Monte Carlo sampling. The added expense of this method is the extra memory required to track which segments have been sampled while the simulation runs. (Compared to most simulation results, this extra overhead is minor.)

Use Latin Hypercube sampling when you are concerned primarily with the accuracy of the simulation statistics.