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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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Ray Koopman

Posts: 3,382
Registered: 12/7/04
Re: Monte Carlo simulation with inequality constraints
Posted: Mar 22, 2012 2:24 AM
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On Mar 19, 3:38 am, deltaquattro <deltaquat...@gmail.com> wrote:
> Il giorno sabato 17 marzo 2012 00:52:57 UTC+1, Ray Koopman ha scritto:
> [..]
>

>>>> I'm sending this reply to both groups. Can you reply to crossposts?
>>>
>>> Hi, Ray!
>>>
>>> Thanks a lot for your reply! Let's see, I'm replying to your message,
>>> and then I will see if it appears in both newsgroups.

>>
>> It didn't. I'm sending this reply to both groups, so that
>> sci.stat.math readers will know that the rest of discussion
>> will be in sci.math.num-analysis only.

>
> Ouch! Sorry, but I'm not familiar with this new Google Groups interface.
> Let's keep it here on sci.math.num-analysis, then.


I'm still using the old interface, and will until it disappears.

>
> [..]
>

>> I'm sorry, I guess I wasn't clear. The "desired final distributions"
>> I was referring to are the X distributions, not the Y. In particular,
>> what I was hoping for was some idea of how much the X1,X2 (and X3,X4)
>> marginal distributions overlap. If the overlap is small then it
>> probably doesn't matter much how you implement the inequality
>> constraints, but if the overlap is large then it seems more likely

>
> Hi, Ray!
>
> You were crystal clear :) but maybe I wasn't! I understood that
> you were speaking about the Xs, i.e., the geometrical parameters
> of the machine, and not the Ys, i.e., the performance of the
> machine as computed by the performance computation code (PCC for
> short). Let's make a pratictal example. I cannot go into the
> details of the real design on a public newsgroup, but I'll give
> you the main idea. Let's suppose that we are manufacturing a tube
> of circular cross-section, and that X1=D1 and X2=D2 are the
> radiuses at inlet and outlet of the tube. The design values of
> D1 and D2 are the same, but, because of manufacturing process
> variability, on some tubes D1 may be smaller than D2, and on
> some others it may be bigger. Unfortunately, PCC doesn't run when
> D1 < D2(!), so I have to discard those cases. Since D1 and D2
> have the same design value and the same manufacturing process,
> their distributions may even be the same, so they're completely
> overlapping! That's why I guess that, with rejection, I should
> discard 1 every 2 runs: because 50% of the times D1 will come out
> smaller than D2, and 50% of the times it will come out bigger.
>
> Of course this is the worst case scenario: for most designs, D1
> and D2 have design values which differ by much more that |U-L|,
> so the probability of the event {D1<D2} is negligible. In these
> cases, I just discard the few runs where PCC fails, and just use
> the rest of the runs to get the distributions of the Ys. However,
> there are designs where D1=D2, so I should know what to do for
> these ones.
>

>> to matter. Could you give us some sample (L,T,U) values? Is the only
>> shape arequirement that the distributions be roughly symmetric and
>> unimodal? Are there any "hard" limits, such as 0, then *must* be met?

>
> 1. L=0.1146515, T=0.11471, U=0.1150025, p=0.022750132
> (p is the probability of X being less than L or more than U)
> 2. The distributions are not always symmetric: sometimes, the
> distribution is quite skewed, and in those cases the Beta
> distribution proves to fit the experimental data better than
> the normal distribution.
> 3. in theory yes, but in practice it doesn't matter. I mean,
> of course a diameter can't be 0 or less. However, the (L,T,U,p)
> values are such that the Monte Carlo code never generates a
> negative diameter even if I use a "unlimited" distribution such
> as the normal one.


Might it be that whoever wrote the PCC knew what he was doing and
assumed that the users of the program would know all the same tricks?
It's hard for me to put this intelligibly when I have no idea what
the code is supposed to be doing, but are there any symmetries that
he might have assumed the users would be aware of, so that if you
interchange certain input values then you just have to interchange
or reverse or complement or ... certain values in the output?



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