Re: interpretation of fit errors

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

On 05/05/2011 05:33 AM, Bastian Märkisch wrote:
>
>  > 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.
>  > (snip)
>
> The point of the original report is the following: After the actual fit
> the calculated errors of free variables are currently scaled by
> FIT_STDFIT. This is correct if there was no error column given for the
> dependent variable, or the errors are in fact relative weights, ie. they
> only give the relative "credibility" of the data points. This would be
> the behaviour of "set fit relativeerrors".

When you say "or" here, are you giving alternate explanation for what it 
means when there is no error column given?  Or do you mean an alternate 
case?  I'm somewhat perplexed by the term "relative".  Scaling by a 
standard deviation to me seems like a normalization process.  Is this a 
well-known technique in the fitting field?  If so, maybe a name related 
to that would help the user understand.

Credibility of the data points is more an interpretation of the 
application.  That's a measurement error sort of thing, isn't it?  (As 
opposed to actual randomness in the quantity itself.)


> If the error column actually contains (absolute) data errors, e.g.
> statistical errors, this scaling is undesirable. "set fit
> absoluteerrors" would allow the user to switch it off and therefore
> obtain the same errors as e.g. CERN Minuit does.
>
> This issue has been discussed at lengths on this mailing list (and
> elsewhere) several times already, see e.g.:
>
> http://thread.gmane.org/gmane.comp.graphics.gnuplot.devel/3737/focus=3740

I read a bit, but didn't get much smarter.  I didn't spend too much time 
on it though.


> and
> http://thread.gmane.org/gmane.comp.graphics.gnuplot.devel/6205
>
> The proposed solution leaves the decision on how to interpret data
> errors to the user. (My gnuplot.ini will certainly have "set fit abs" in
> it.) For the sake of compatibility and since "weigths" are standard in
> some fields, the default stays like it is.

Is this change significant?  Is this an iterative process where the 
resulting errors are fed back into the computations to improve the fit? 
  If so, then I'd say backward compatibility is important.

But if it is some nuanced detailed that initially could be seen as a 
mistake in coding, then I'd say backward compatibility isn't so much an 
issue.

My fear with this is that a user could run the fit, get the results and 
significantly misinterpret what they mean by assuming errors were 
expressed as scaled or unscaled.  That's especially troublesome if the 
standard deviation FIT_STDFIT is near 1.0 because its effect might not 
be so apparent to the user.  You are saying "(My gnuplot.ini will 
certainly have "set fit abs" in it.)", so you think of the errors in one 
way.  Others may think another way, apparently.  So, if using the 
expression "errors" in fitting is in any way ambiguous, it might be best 
to always refer to "absolute errors" or "relative (normalized?) errors". 
  I.e., gnuplot shouldn't input or report something as just "errors".

That probably didn't help any; I'm just trying to brainstorm how to 
clear this up.

Dan