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Thoughts on the number of runs in Monte Carlo simulation

Yaohua2024

Hi, I have been reading up on 3 sigma from this wikipedia article. https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule

In this article, you can see the following table that lists the probability of occurrence for different sigmas. 

If my PDK models with plus, minus 3 sigma then does that mean I just need to do 370 runs in Monte Carlo simulation to capture a full picture? If we have a very small number of runs, then the Monte Carlo simulation result may not mean much, so we should have a bigger number of runs, but this will increase simulation time.

Am I right in thinking that 370 runs is a good compromise between simulation time and accuracy?

Thanks,

YH

Parents

  • Hi YH,

    It depends which info you want to extract from the MC run. If you just want to see your distribution or approx. values of mean and standard deviation, that's fine. Anyway, note that those numbers will get more accurate as you increase the number of runs.

    On the other hand, if you want to extract a few outliers that you would later run separately, you probably need to go beyond 370. If the occurrence is 1 in 370, that does not mean that you will certainly get that one outlier in the sample space of 370. I mean you can toss a coin 10 times and not once get a head (the probability is not 100%, but something like 99.9% for the coin example, you could ask ChatGPT for the exact number). I think you have something like 60-70% chances to get one outlier in these 370 samples, so I would personally run at least 1000. 

    BR

    /Janko 

Reply

  • Hi YH,

    It depends which info you want to extract from the MC run. If you just want to see your distribution or approx. values of mean and standard deviation, that's fine. Anyway, note that those numbers will get more accurate as you increase the number of runs.

    On the other hand, if you want to extract a few outliers that you would later run separately, you probably need to go beyond 370. If the occurrence is 1 in 370, that does not mean that you will certainly get that one outlier in the sample space of 370. I mean you can toss a coin 10 times and not once get a head (the probability is not 100%, but something like 99.9% for the coin example, you could ask ChatGPT for the exact number). I think you have something like 60-70% chances to get one outlier in these 370 samples, so I would personally run at least 1000. 

    BR

    /Janko 

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