Stochastic models

Have I run enough simulations?

The optimal number of simulations is reached when results stabilize, showing approximate convergence. This means additional simulations don’t significantly change the outcome. See Figure 7.1 for a demonstration of this convergence.

Steps to calculate the needed number of simulations [source]:

1. Run the simulation with a default number of runs \(R_0\) (usually \(R_0 = 1000\)). Now you should have a vector with the results \(x_0\) where \(\text{length}(x_0) = R_0\).

2. Calculate the mean value \(\overline{x_0}\) and standard deviation \(\sigma_0\).

3. Specify the allowed level of error \(\epsilon\) and the uncertainty \(\alpha\) you are willing to accept. Normally you choose \(\epsilon = \alpha = 0.05\%\).

4. Use this equation to get the required number of simulations:

\[R \geq \left( \frac{Z_{1 - \frac{\alpha}{2}} \times \sigma_0}{\epsilon \times x_0} \right)^2\]

5. Use the Student t-distribution rather than the normal distribution for small \(R_0\).

the output doesn’t change much if the model was run with more simulations