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Topic: Monte Carlo simulation with inequality constraints
Replies: 11   Last Post: Mar 23, 2012 8:53 AM

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deltaquattro@gmail.com

Posts: 77
Registered: 7/21/06
Monte Carlo simulation with inequality constraints
Posted: Mar 15, 2012 6:21 AM
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Hi, all,

I've been given a computer codes with some input variables X1,...Xn and some outputs Y1,...Ym. I want to use a Monte Carlo code to compute the distributions of the Ys, given some distributions for the Xs. The Xs are geometrical parameters of an industrial design, and as a first approximation they are considered independent. Unfortunately the code doesn't run when X1<X2 or X3<X4, so I need to impose the two constraints X1>=X2 and X3>=X4.
How can I do it? I'd prefer a solution which is valid for general distributions, but I can also accept one which works when the Xs are normally distributed.

Some ideas which sprung to my mind:
1. My Monte Carlo code allows to define a linear correlation matrix for the input variables: I don't see how this helps, but maybe you do :)
2. I let the Monte Carlo code to generate freely the sample runs, and whenever a run has X1<X2 or X3<X4, I discard it. However, I'm worried that this "rejection process" may distort the distributions of the Xs. Also, I guess I'll need to perform four times as many Monte Carlo runs as usual, to have the same level of statistical convergence.
3. I change my Monte Carlo variables: instead than X1 and X3, I use Z1 = |X1-X2| and Z2=|X3-X4|. This way, X1 = X2 + Z1 >= X2, and X3 = X4 + Z2 >= X4. However, while I was able to make some reasonable assumptions on the distributions of the original variables, now I have no idea which distributions I should use for Z1 and Z2...Thanks,

Best Regards,

deltaquattro

ps apologies for the double posts, but I'm not sure which ng is more suitable for this thread, and I'm not able to create a crosspost with Google Groups.



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