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Re: Errors from FindFit

• To: mathgroup at smc.vnet.net
• Subject: [mg57169] Re: [mg57166] Errors from FindFit
• From: frank at kuesterei.ch (Frank Küster)
• Date: Fri, 20 May 2005 04:43:03 -0400 (EDT)
• References: <200505190709.DAA13170@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

phrje at warwick.ac.uk (Don Paul) wrote:

> Is there a simple way to place accuracies on the fitted quantities
> calculated by FindFit? I've read the documentation but can't see how to
> get there. Seems strange to have done all that work and not estimate how
> accurate the final result maybe.

The reason why it doesn't give errors might be that this is not a
trivial task.  NonLinearRegress gives some additional information,
however you cannot simply take these as the standard error of your
fitted parameter.

First of all, are you sure that that the error is really in the fitted
dataset, and not between different datasets - i.e. perhaps you should
rather repeat your sample preparation, experimental setup and data
acquisition, fit the other acquired datasets, too, and take the average
and stddev of the fitted parameters of all datasets?

Second, in a Fit with only one parameter, it is quite straightforward to
tell in which range of the parameter the fit is still acceptable
(i.e. the increase in \Chi^2 cannot be excluded to be random on a N%
confidence level, giving a N% confidence level of the parameter error).
But if you have multiple parameters, you have to take the mutual
dependencies into account, and AFAIK it is not even uncontroversial how
to get numbers for errors in this case (options are to take the values
derived from the curvature of the \Chi^2 surface, to compute \Chi^2 when
varying one parameter and keeping the others fixed, or letting them
float, or even do Monte Carlo jumps around the minimum).

NonLinearRegress has some explanations about this, and probably you (and
I) should read the references given there...

Regards, Frank
-- 
Frank Küster
Inst. f. Biochemie der Univ. Zürich
Debian Developer

• Follow-Ups:
  • Re: Re: Errors from FindFit
    • From: DrBob <drbob@bigfoot.com>

• References:
  • Errors from FindFit
    • From: phrje@warwick.ac.uk (Don Paul)