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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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AMX

Posts: 35
Registered: 8/22/09
Re: Monte Carlo simulation with inequality constraints
Posted: Mar 16, 2012 1:31 PM
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On Thu, 15 Mar 2012 03:21:01 -0700 (PDT),
deltaquattro <deltaquattro@gmail.com> wrote:

> Hi, all,
>


> I want to use a Monte Carlo code [..for..] given some
> distributions for the Xs.


> The Xs are geometrical parameters of an industrial design, and
> as a first approximation they are considered independent.


> I need to impose the two constraints X1>=X2 and X3>=X4.

> 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.
>


Suppouse a bit simpler case, only X1 and X2. Let constraints are
0<=X1<=1, 0<=X2<=1. On the plane it gives a quadrangle. Let both
are normally distributed, what implies some average, assume equal
to 0.5.

It is quite easy to imagine distribution of points, small bullets
filled with colour shooted to this quadrangle would give very
clear pattern, with dense dots around (0.5,0.5) and more
distant dots away from center.

For uniform distribution of Xs dots are also located almost
equally.

Now introduce additional constraint (e.g. X1>X2). We have a triangle and
shooting gives similar resuls, dense dots around center (defined
by average of Xs) but now pattern depends on relation of
axis and triangle. Unlike for uniform distribution, where dots
are still equally distributed.

Which pattern better reflects reality, it give better model.

For me two question are most important:

- are Xs normally distributed (as industrial parameters)?
- where is the average of each Xs?

AMX




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