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)