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Re: Filtering data from numerical minimization

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116415] Re: Filtering data from numerical minimization
  • From: Ray Koopman <koopman at sfu.ca>
  • Date: Mon, 14 Feb 2011 04:26:57 -0500 (EST)

On Sun, 13 Feb 2011 at 04:49:45 -0800 (PST), 
Sebastian <sebhofer at gmail.com> wrote:
   [Ray Koopman wrote:]
>> ...
>> It sounds like you're doing nonlinear regression and you have a fair
>> number of dependent-variable outliers, on the order of 20%. The usual
>> approach to such situations is to do some form of robust regression,
>> that minimizes something other than the unweighted sum of squared
>> residuals. There are many possibilities. Can you be more specific
>> about your model?
>
> Thanks for your answer. I tried using the algorithm you suggested,
> but a simple MovingMedian gives me "nicer" results.
> I have to admit that I have no clue what you are talking about in your
> second post (I'm not even sure if it really applies to my specific
> problem, but I'm happy to learn about it, if it actually does!),
> so I just try to clear one thing up:
> In my original post I may have not been complete clear about the fact
> that my function f is actually a deterministic, analytically given
> function, which I try to minimize numerically. The "noise" is
> introduced by the minimization which fails to find the correct optimal
> value! So another way of solving my problems would be by improving the
> way I do the minimization. I just thought that this may not be
> possible.
> Does this actually provide new information to you...?
> I'm sorry, I'm a little lost here...
> 
> Thanks for your effort!
> Sebastian

OK, I think I understand the situation now. You're not doing 
nonlinear regression, so my previous post was irrelevant and 
misleading. Ignore it.

Try increasing WorkingPrecision, AccuracyGoal, and PrecisionGoal. 
Also, try a different Method. If that doesn't fix things, try using 
better starting intervals. This may take two passes thru the list 
1...N. On the first pass, use your best a priori guess. On the 
second pass, take the results from n-1 and n+1 on the previous pass 
as the starting intervals for n. Take whichever results (pass 1 or 2)
give a lower fmin. Iterate (pass 3,4,...) until it stabilizes.


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