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s-soberh1-Visitor
1-Visitor
August 24, 2018
Question

Can a Monte Carlo simulation converge?

  • August 24, 2018
  • 3 replies
  • 10788 views

Hello,

 

I'm currently performing Monte-Carlo-Simulations by using Mathcad Prime 4.0. When I change the number of events, I always get different values. Should an Monte-Carlo-Simulation not converge with a higher number of events to a certain value?

 

 

3 replies

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
August 24, 2018

Can you show your Mathcad Prime 4 sheet?

S
s-soberh1-VisitorAuthor
1-Visitor
August 24, 2018

Hello,

 

on Monday I could share my program because I'm not at the university at the weekend. But maybe it helps you that the process is exactly the same as described in the help (monte-carlo example).

D
DJF16-Pearl
16-Pearl
August 24, 2018

It should, yes.  It can often take 10000 to get a good distribution shape for some problems.  Although I do question Mathcad's random number generator sometimes.  I know it's gotten stuck before and I had to shut it down to get fresh values.  Also playing with the histogram interval setting can change the apparent shape.

    L
    LucMeekes23-Emerald IV
    23-Emerald IV
    August 24, 2018
    NO! Certainly not!
    Convergence is not a term that I think is used with stochastic processes. You can get convergence by iteration. With increasing the number of runs in Monte Carlo you will more likely get Divergence.
    Example: if you throw dice over and over again, the same numbers from 1 to 6 will reappear, no matter how often you throw. It's not that when you've thrown dice 1 million times, the number three will stand out for example.
    If you have a system with 10 parameters that each in some way determine an output value, and each parameter has a certain distribution of randomness, the more often you calculate the output value from randomly chosen parameters, each within its own distribution, the more likely you will find output values closer to the edge. So output values spread out, rather than coming closer.
    What you will get, if you plot a histogram of the output values, is a better approximation of the distribution shape.
    But note that the more input parameters you have and the higher the number of runs, the closer the distribution of the output values will tend to a normal=Gaussian distribution. And the perfect Gaussian distribution can reach all values from minus to plus infinity. Divergence, not convergence!
    On the other hand it will allow you to appromate the expected value of the distribution more accurately, just by calculating the mean...
    So if you're looking for the expected value, increasing the number of runs may be a good idea. But never expect the output values to converge to a number.


    Success!
    Luc
    D
    DJF16-Pearl
    16-Pearl
    August 24, 2018

    Maybe convergence isn't the right mathematical terminology, but as I interpret the question, I think it's a question on if most monte carlos will 'converge' to a stable distributed shape.  In that case the answer is usually yes.  With 5 runs the shape is erratic, with 1E6 it usually isn't.  Similarly, a monte carlo is famously used to solve for pi, and the more runs you perform the closer you get - so it can converge. 

     

    And since items are bound in reality (e.g. dimensions on a print) actual divergence to infinity is something I don't need to consider when wearing my engineering hat.  

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