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filipe Junior Member Offline Posts: 22 Brasil	number of runs in Monte carlo simulation Feb 10^th, 2009, 2:40am Hi, How to estimate the minimum number of runs in a Monte carlo simulation??? I heard that this estimation can be calculated based on the central limit theorem. Thanks Filipe
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boe Community Fellow Offline Posts: 615	Re: number of runs in Monte carlo simulation Reply #1 - Feb 10^th, 2009, 3:59am Hi Filipe, sigma/sqrt(N) is a measure for the accuracy of the average because averaging N normally distributed random variables reduces the standard deviation by a factor of sqrt(N). [Edit: derived from Central limit theorem] BOE
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vivkr

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Re: number of runs in Monte carlo simulation
Reply #2 - Feb 12^th, 2009, 12:16am

Maybe a more concrete number for you. Typically, we are trying to estimate the moments of the distribution for a given parameter (mean and standard deviation) within a certain confidence level.

As a benchmark, 100 runs of Monte Carlo will typically give +/-2% accuracy in estimation of mean, and +/- 14% accuracy in estimation of the standard deviation. Doubling the number of runs will improve the accuracy by sqrt(2).

Best regards,

Vivek

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Andrew Beckett Senior Fellow Offline Life, don't talk to me about Life... Posts: 1742 Bracknell, UK	Re: number of runs in Monte carlo simulation Reply #3 - Feb 12^th, 2009, 1:20pm Note also that spectre supports "Latin Hypercube Sampling" these days which tends to converge the standard deviation with fewer samples http://en.wikipedia.org/wiki/Latin_hypercube. Regards, Andrew.
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filipe

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Brasil

Re: number of runs in Monte carlo simulation
Reply #4 - Feb 16^th, 2009, 10:31am

Vivkr,

This is exactly my question. How can I calculate the accuracy of the mean and standard deviation? When can I find an explanation about it?

Thanks a lot
Filipe

vivkr wrote on Feb 12^th, 2009, 12:16am:

Maybe a more concrete number for you. Typically, we are trying to estimate the moments of the distribution for a given parameter (mean and standard deviation) within a certain confidence level.

As a benchmark, 100 runs of Monte Carlo will typically give +/-2% accuracy in estimation of mean, and +/- 14% accuracy in estimation of the standard deviation. Doubling the number of runs will improve the accuracy by sqrt(2).

Best regards,

Vivek

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packiaraj

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India

Re: number of runs in Monte carlo simulation
Reply #5 - Feb 27^th, 2009, 6:09am

Filipe,

Guess you must have seen this link by now: Roll Eyes

http://www.financial-risk-manager.com/risks/market/mc_errors.html

The expression for error-in-"Mean" that you get from MC sims. BOE has indicated it almost correctly, though it is for only 1Sigma (~68% confidence-level in Normal Distribution).

Think we have to add this error-in-"Mean" to actual "Mean" when we say this is my Bandgap-output or Oscillator-frequency accuracy.

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analogue_guy

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Re: number of runs in Monte carlo simulation
Reply #6 - Mar 2^nd, 2009, 12:43pm

filipe wrote on Feb 16^th, 2009, 10:31am:

Vivkr,

This is exactly my question. How can I calculate the accuracy of the mean and standard deviation? When can I find an explanation about it?

Thanks a lot
Filipe

After running the Monte Carlos and collecting the results you can calculate confidence interval for mean,sigma.

One is based on Student-t deviation, the other is based on CHI-SQUARE deviation. You can find more details in every basic statistics books.

If you would like, I could look up the equations.

Cheers

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AnalogDE Senior Member Offline Posts: 137	Re: number of runs in Monte carlo simulation Reply #7 - Mar 19^th, 2009, 4:43pm analogue_guy, Could you please send me or post the equations and/or a reference that has this information? I'm also interested. Thanks!
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