methods - How many simulations need to do?

Question

Hello my problem is more related with the validation of a model. I have done a program in netlogo that i'm gonna use in a report for my thesis but now the question is, how many repetitions (simulations) i need to do for justify my results? I already have read some methods using statistical approach and my colleagues have suggested me some nice mathematical operations, but i also want to know from people who works with computational models what kind of statistical test or mathematical method used to know that.

Answer 1

There are two aspects to this (1) How many parameter combinations (2) How many runs for each parameter combination.

(1) Generally you would do experiments, where you vary some of your input parameter values and see how some model output changes. Take the well known Schelling segregation model as an example, you would vary the tolerance value and see how the segregation index is affected. In this case you might vary the tolerance from 0 to 1 by 0.01 (if you want discrete) or you could just take 100 different random values in the range [0,1]. This is a matter of experimental design and is entirely affected by how fine you wish to examine your parameter space.

(2) For each experimental value, you also need to run multiple simulations so that you can can calculate the average and reduce the impact of randomness in the simulation run. For example, say you ran the model with a value of 3 for your input parameter (whatever it means) and got a result of 125. How do you know whether the 'real' answer is 125 or something else. If you ran it 10 times and got 10 different numbers in the range 124.8 to 125.2 then 125 is not an unreasonable estimate. If you ran it 10 times and got numbers ranging from 50 to 500, then 125 is not a useful result to report.

The number of runs for each experiment set depends on the variability of the output and your tolerance. Even the 124.8 to 125.2 is not useful if you want to be able to estimate to 1 decimal place. Look up 'standard error of the mean' in any statistics text book. Basically, if you do N runs, then a 95% confidence interval for the result is the average of the results for your N runs plus/minus 1.96 x standard deviation of the results / sqrt(N). If you want a narrower confidence interval, you need more runs.

The other thing to consider is that if you are looking for a relationship over the parameter space, then you need fewer runs at each point than if you are trying to do a point estimate of the result.