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Re: Re: Errors from FindFit

• To: mathgroup at smc.vnet.net
• Subject: [mg57221] Re: [mg57169] Re: [mg57166] Errors from FindFit
• From: DrBob <drbob at bigfoot.com>
• Date: Sat, 21 May 2005 02:39:39 -0400 (EDT)
• Organization: Deep Space Corps of Engineers
• References: <200505190709.DAA13170@smc.vnet.net> <200505200843.EAA00465@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

In addition to all those considerations, there's no reason to think Chi-square or Gaussian probability measures apply to nonlinear fits of arbitrary data. If you DO know what the error distribution should be, that affects how a fit should be determined, and the built-in probably won't do it for you.

Bobby

On Fri, 20 May 2005 04:43:03 -0400 (EDT), Frank Küster <frank at kuesterei.ch> wrote:

> 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



-- 
DrBob at bigfoot.com

• References:
  • Errors from FindFit
    • From: phrje@warwick.ac.uk (Don Paul)
  • Re: Errors from FindFit
    • From: frank@kuesterei.ch (Frank Küster)