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From: <HIDDEN>
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Subject: Re: creating loops for a large system of variables
Date: Mon, 04 Apr 2011 09:48:42 -0500
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On 4/3/2011 11:34 PM, dpb wrote:
> On 4/3/2011 11:13 PM, Nate Jensen wrote:
>>> Or "Latin-Hypercube Sampling" is another buzzword
>>>
>>> More actual detail of what is needed could undoubtedly help cull the
>>> general to at least a little more specific.
>>>
>>> --
>>
>> What I need to do is understand the behavior of my system as different
>> design variables are changed within it.
>>
>> Although I could run each case independently, it would be to my
>> advantage to compare them to one another in one run. At the moment,
>> optimization or inverse design of the inputs, would be much more
>> difficult, due to their complex, and at times rigid, nature. The main
>> caveat that I have is that, many of the inputs depend upon one another,
>> and may or may not be changed depending upon the design. This all sums
>> up to the ability to change various inputs depending on the design of
>> the system, and compare their outputs.

>>
>> I am regretful that I am not making myself clear.
>
> No, that's pretty clear. Read up on response surfaces as one possible
> tool--if the models aren't terribly nonlinear. Steven L's pointers are
> in similar direction.
>
> DOE is the exercise in setting up criteria based on combination of what
> is known of the model and the desired estimators to try to help in an
> efficient use of the number of points and values for the independent
> variables of those points that meet specific design criteria regarding
> which effects may be estimated w/o confounding, which effects are
> possibly sacrificed or confounded w/ others to reduce the design size,
> etc., etc., ...
>
> If this is academic exercise, if you have access to a statistician it
> would be _a_good_thing_ (tm)....
>
...

And to make Steve's and my point explicit...if you have 25 variables to 
study and you only use two levels for each, that's 2^25 total cases in 
the simplistic approach or 33554432 runs of the model.  If there's any 
nonlinearity at all in the model you need a minimum of three levels to 
see it or 3^25 ~ 8.5E11.  I don't think you'd be able to interpret the 
results even if you could run all those cases.

So, you need a smarter approach.

--