How many times should we conduct the experiment to ensure that the estimation errors are least?
Are you asking about the number of simulations or the sample size for the observed data?
Both the simulation and the sample will converge to the population value. Convergence does not mean equal. In converging, the result gets closer and closer to the "true" answer, but it might never be equal to the "true" answer.
It is not clear what the true answer really is.
The population is a sample from an underlying distribution.
The observed data are a sample from the population.
You are now two steps removed from the underlying distribution. If you can assume that the population is infinite, then the distribution of the population will equal the underlying distribution.
The answer also depends on what kind of Monte Carlo simulations you are running.
Also, if you have a small sample from a small popilation, no amount of Monte Carlo simulation will save you.
Will this work?
1) Run the simulation with a sample size of 5.
2) Repeat #1 a thousand times.
3) Repeat #1, but increase the sample size to 50, and again with 500, and finally with 5000. Fill in or extend to larger sample sizes as needed.
Assuming that the system converges, what you should end up with is a statistic of interest that converges to some value. Also, the run-to-run variability in the statistic should decrease (likely by a factor of the inverse square root of the sample size).
By running a regression analysis of the variability in the statistic as a function of sample size, you should be able to estimate a sample size that will result in any level of convergence that you wish. It also justifies a specific sample size.
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size