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Re: fitting from x to y and from y to x

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Op dinsdag 4 februari 2014 21:06:56 UTC+1 schreef Ethan A Merritt:
> Jean Dupont wrote:
> 
> 
> 
> > It happens quite often that one is measuring two data sets, lets call them
> 
> > x and y. It's common also to have a measurement error on x (delta_x) and
> 
> > on y (delta_y). Then a fitting on f(x) with some parameters (a, b, c...)is
> 
> > performed using delta_y which when done properly will give reliable values
> 
> > for a, b, c... It's also interesting however to fit the inverse function
> 
> > of f(x) with y as independent variable and x as dependent variable using
> 
> > delta_x in the fitting. This will give slightly different values for a,b,c
> 
> > ...One could then take the mean of both sets a,b,c for an end-result.
> 
> > 
> 
> > I was wondering whether the procedure above can be implemented elegantly
> 
> > in Gnuplot without having to calculate the inverse function explicitly
> 
> > first.
> 
> 
> 
> This has been discussed before several times.  See for example
> 
>  http://gnuplot.10905.n7.nabble.com/fit-NLLS-and-Levenberg-Marquardt-td9090.html
> 
> 
> 
> No, you don't necessarily need to have inverse functions defined.
> 
> However in order to allow properly for errors on x you need a 
> 
> different treatment of the minimization procedure.
> 
> I would use a maximum-likelihood approach. 
> 
> This is not built into gnuplot, but if a search will probably turn
> 
> up examples of incorporating gnuplot into the process.
> 
> I found this example in just a few minutes of looking:
> 
> 
> 
>  http://nbviewer.ipython.org/github/fonnesbeck/Bios366/blob/master/notebooks/Section3_1-Univariate-and-Multivariate-Optimization.ipynb
> 
> 
> 
> 	Ethan
Thank you Ethan for this very interesting reply

kind regards,
jean

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fitting from x to y and from y to x Jean Dupont <jeandupont115@gmail.com> - 2014-02-04 01:29 -0800
  Re: fitting from x to y and from y to x Karl <mail.kfr@gmx.net> - 2014-02-04 13:05 +0100
    Re: fitting from x to y and from y to x Jean Dupont <jeandupont115@gmail.com> - 2014-02-04 06:57 -0800
  Re: fitting from x to y and from y to x Ethan A Merritt <merritt@u.washington.edu> - 2014-02-04 12:06 -0800
    Re: fitting from x to y and from y to x Jean Dupont <jeandupont115@gmail.com> - 2014-02-05 06:59 -0800
      Re: fitting from x to y and from y to x Ethan A Merritt <EAMerritt@gmail.com> - 2014-02-05 08:12 -0800
        Re: fitting from x to y and from y to x Jean Dupont <jeandupont314@gmail.com> - 2014-02-06 11:54 -0800

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