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Groups > comp.graphics.apps.gnuplot > #2293

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

From Ethan A Merritt <EAMerritt@gmail.com>
Newsgroups comp.graphics.apps.gnuplot
Subject Re: fitting from x to y and from y to x
Date 2014-02-05 08:12 -0800
Organization made entirely of Lego
Message-ID <lctnpr$24f$1@dont-email.me> (permalink)
References <ff8c63b2-6c6a-406f-b109-53e535b59ddd@googlegroups.com> <lcrh92$9mh$1@dont-email.me> <c3130ce1-a4f8-4a04-950f-fd7313a7cbc2@googlegroups.com>

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Jean Dupont wrote:

> 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

I forgot to mention that there is a patch against current gnuplot
on the SourceForge tracker that adds a new fitting mode that can
use error estimates on both x and y.  I have not looked at this
myself, but I would be interested in hearing from test users.
It is more likely to be included in a future gnuplot version if
there are multiple people advocating for it.

https://sourceforge.net/p/gnuplot/patches/585/

The patch is based on the "effective variance method" 
(Jay Orear, Am. J. Phys., Vol. 50, No. 10, October 1982)

	Ethan


> 
> kind regards,
> jean

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Thread

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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