Simulation Sampling Methods

During each trial of a simulation, the sampling method selects a random value for each assumption in your model.

Strategic Modeling simulations use one of these sampling methods:

• Monte Carlo—Randomly selects any value from the defined distribution of each assumption.

• Latin Hypercube—Randomly selects values and spreads them evenly over the defined distribution of each assumption.

Monte Carlo Sampling

Monte Carlo simulation randomly and repeatedly generates values for uncertain variables to simulate a model. The values for each assumption’s probability distribution are random and totally independent. In other words, the random value selected for one trial has no effect on the next random value generated.

Monte Carlo simulation was named for Monte Carlo, Monaco, whose casinos feature games of chance such as roulette, dice, and slot machines, all of which exhibit random behavior.

Such random behavior is similar to how Monte Carlo simulation selects variable values at random to simulate a model. When you roll a die, you know that a 1, 2, 3, 4, 5, or 6 will come up, but you do not know which for any particular trial. It's the same with the variables that have a known range of values and an uncertain value for any particular time or event (for example, interest rates, staffing needs, stock prices, inventory, phone calls per minute).

Using Monte Carlo sampling to approximate the true shape of the distribution requires more trials than Latin Hypercube.

Use Monte Carlo sampling to simulate real world what-if scenarios for your model.

Latin Hypercube Sampling

Latin Hypercube sampling divides each assumption’s probability distribution into  non-overlapping segments, each having equal probability.

While a simulation runs, Latin Hypercube 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 has sampled each segment exactly once, the process repeats until the simulation stops.

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.