Selecting the Sample Size

Each probabilistic value is simulated by computing a random sample of values from the actual probability distribution.

You can control the sampling method and sample size by using the Uncertainty setup dialog. This appendix briefly discusses how to select a sample size.

Choosing an Appropriate Sample Size

There is a clear trade-off for using a larger sample size in calculating an uncertainty variable. When you set the sample size to a large value, the result is less noisy, but it takes a longer time to compute the distribution. For an initial probabilistic calculation, a sample size of 20 to 50 is usually adequate.

How should you choose the sample size m? It depends both on the cost of each model run, and what you want the results for. An advantage of the Monte Carlo method is that you can apply many standard statistical techniques to estimate the precision of estimates of the output distribution. This is because the generated sample of values for each output variable is a random sample from the true probability distribution for that variable.

Uncertainty about the Mean

First, suppose you are primarily interested in the precision of the mean of your output variable y. Assume you have a random sample of m output values generated by Monte Carlo simulation:

(y₁, y₂, y₃, …y_m)

You can estimate the mean and standard deviation of y using the following equations:

[math]\displaystyle{ \vec y=\sum_{i=1}^m \frac { y_i }m }[/math]

[math]\displaystyle{ s^2=\sum_{i=1}^m \frac { (y_i - \vec y)^2} {m - 1} }[/math]

This leads to the following confidence interval with confidence α, where c is the deviation for the unit normally enclosing probability α: