Re: NonlinearFit

• 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: <7r24q2\$6qd@smc.vnet.net>
• 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
>
>
>
Dear 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).

KR,

Peter

```

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