Re: Cash statistic fitting bug?

On Tue, Jul 30, 2013 at 18:04 +0200, Moritz Boeck wrote:
> Dear isis users,
> 
> a warning for those of you who use the Cash statistic in isis:
> It seems that this statistic in combination with a gradient
> minimization algorithm (at the moment we just verified it with the
> lmdif and mpfit fit method) leads to (slightly) wrong best fit
> parameter values.
[...]
> So far we did not look in detail for the source of the problem. The
> easiest way for us to avoid the problem was using the Cash statistic
> with another minimization algorithm, such as the "powell" method.
> 
> We appreciate any suggestions.

This limitation of mpfit is noted in the mpfit help page which
says:

 DESCRIPTION
    The mpfit Levenberg-Marquardt algorithm is the default
    minimization algorithm used in fitting models to data.  This
    algorithm was derived under the assumption that the function to
    be minimized is the Chi-square fit-statistic.

Also, since lmdif invokes mpfit with a reduced set of options
for back-compatibility, the same limitation applies (see the
lmdif help page).

While one can derive an LM-type algorithm for the Cash
statistic, isis currently does not provide that option.

Thanks,
-John
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