From: Ingo Thies <ingo.thies@gmx.de>
Newsgroups: comp.graphics.apps.gnuplot
Subject: Fitting: How does gnuplot calculate the covariance matrix?
Date: Fri, 08 Apr 2011 13:05:01 +0200
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Hi all,

I am trying to find out how exactly gnuplot calculates the covariance
matrix for a fitted function.

The background: I am still mistrusting the error ellipses one gets from
the eigenvalues. As already mentioned last year (aroung May or so), I
suspect that the resulting error contours are underestimated since the
best-fit chi^2 is assumed to be zero there, but it isn't.

I have compared the error ellipses with the true error contours from an
independent chi^2-2D-mapping routine, and found that the latter may be
considerably larger than the ones one would get from gnuplot's cov matrix.

However, basic information about covariance (e.g. from Wikipedia) are
misleading here, since they only deal with the covariance of measured
data themselves, not the errors. Also I didn't manage to get a clear
image from the sourcecode yet.

For the long term, it would be helpful to include the basic formulas and
the most important caveats and pitfalls (e.g. how may I trust the
results or not) into the gnuplot.pdf.

In our institute, there are people working with gnuplot and its fitting
algorihm, but lack of important information about how they are working
in detail.

Many thanks for any helpful reply!

-- 
Gruß,
      Ingo