- To: mathgroup at smc.vnet.net
- Subject: [mg19700] Re: NonlinearFit
- From: peter.buttgereit at pironet.de (Peter Buttgereit)
- Date: Sat, 11 Sep 1999 16:36:05 -0400
- Organization: communication works
- References: <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
[This followup was posted to comp.soft-sys.math.mathematica and a copy
was sent to the cited author.]
In article <7r24q2$6qd at smc.vnet.net>, virgil.stokes at neuro.ki.se says...
> In reference to Statistics `NonlinearFit` (vers. 1.4, author: John M. Novak)
> for Mathematica Version 3.0.
> I would like to be able to replace the minimization criterion
> that is currently in this package (least-squares). I am trying to
> find a different type of minimization criterion -- one that
> performs better (hopefully) for my particular problem.
> Is it possible to use this package such that one can override the
> current least-squares criterion with a user defined criterion?
> -- Virgil
As like as William I would be curious about Your ideas other
than least-squares optimisation...
The L-M-Algorithm is essentially least-squares based -- there
is no way to change this criterion.
Also, using absolute distances (or whatever) will complicate
confidence interval estimation considerably.
If You are unhappy with least-squares I suppose You have noisy
data or some problems with "outliers".
In this case You can either "clean up" Your data in advance of
fitting or use a suitable transformation.
I.e. using least-squares fitting on the logarithms of Your data
will minimize over the sum of squares of logarithms of the
deviations -- noisiness and outlier problem are somewhat
reduced if the data model allows for the transformation.
Further, You can define Your own criterion this way:
Fit "the model" using L-M (i.e.)
Define a criterion to be minimised/maximised based on the residuals
(sum, sum of squares, whatever suitable)
and then use FindMinium to optimise over Your criterion.
For me this method was a affordable solution occasionally ( must
have been posted in this group some years ago).
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