Re: interpretation of fit errors

[Daniel J S. <dan...@ie...>]

On 05/05/2011 02:01 AM, Bastian Märkisch wrote:

> Does somebody have a better name for the proposed setting on how to
> interpret data errors? The currently proposed
>
>    set fit relativeerrors|absoluteerrors
>
> sounds a bit odd to me. See bug #2956524
>
>      Bastian

Bastian,

Please fill us in about what these are supposed to mean.  Maybe that 
will lead to better syntax.  Browsing the documentation for "fit" and 
reading the bug report is a bit to digest.  Here is the comment in the 
bug report:

**
Dear gnuplotters,

I may be missing something, but I understood that with least squares 
with given standard deviations, the error in the fit parameters is 
simply the square root of the according covariance matrix diagonal 
element, opposed to the case of unknown standard deviations, where the 
standard deviations are assumed to be equal and are estimated a 
posteriori by chi^2 / ndf. If this is the case, I think lines 766--768 
in fit.c of gnuplot version 4.4 rc1 are a bug, because in the case of 
known data errors, this code should not be exercised.

Thanks for your comments,

Paul
**

The case of "known data errors", what is that?  Does Paul mean known 
statistics for the data errors (i.e., the case where an extra column is 
supplied to the input)?

I see in the documentation something about "set fit errorvariables" and 
variables created with "_err" tagged onto the string.  Is this what 
"relativeerrors" and "absoluteerrors" refers to?  Is it something having 
to do with the way in which "_err" error variables are derived?  If so, 
what then if the user wants both for comparison purposes?  Maybe it 
should become two sets of error variables "_errabs" and "_errrel".  Am I 
on the right track?

As for the original bug report, unless this is something obvious, 
perhaps there is a way to illustrate the error with a test case, to 
ensure the fit is solved correctly.  In fact, a tutorial demo or two 
illustrating settings would be nice.

Dan



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-- 

Dan Sebald
email: daniel(DOT)sebald(AT)ieee(DOT)org
URL: http://www(DOT)dansebald(DOT)com