[SciPy-User] Revisit Unexpected covariance matrix from scipy.optimize.curve_fit

[Tom Aldcroft]

The 0.11 documentation on curve_fit says:

sigma : None or N-length sequence
  If not None, it represents the standard-deviation of ydata. This
vector, if given, will be used as weights in the least-squares
problem.

It unambiguously states that sigma is the standard deviation of ydata,
which is different from a relative weight.  That gives a clear
implication that increasing the standard deviation of all the data
points by some factor should change the parameter covariance.

Can the doc string be changed to say "If not None, it represents the
relative weighting of data points."  I would say that most astronomers
and physicists are likely to be tripped up by this otherwise because
"sigma" has such a well-understood meaning.

- Tom


On Fri, Feb 22, 2013 at 1:03 PM, Pierre Barbier de Reuille
<pierre at barbierdereuille.net> wrote:
> I don't know about this result I must say, do you have a reference?
>
> But intuitively, perr shouldn't change when applying the same weight to all
> the values.
>
> --
> Barbier de Reuille Pierre
>
>
> On 22 February 2013 17:12, Moore, Eric (NIH/NIDDK) [F] <eric.moore2 at nih.gov>
> wrote:
>>
>> > -----Original Message-----
>> > From: Tom Aldcroft [mailto:aldcroft at head.cfa.harvard.edu]
>> > Sent: Friday, February 22, 2013 10:42 AM
>> > To: SciPy Users List
>> > Subject: [SciPy-User] Revisit Unexpected covariance matrix from
>> > scipy.optimize.curve_fit
>> >
>> > In Aug 2011 there was a thread [Unexpected covariance matrix from
>> > scipy.optimize.curve_fit](http://mail.scipy.org/pipermail/scipy-
>> > user/2011-August/030412.html)
>> > where Christoph Deil reported that "scipy.optimize.curve_fit returns
>> > parameter errors that don't scale with sigma, the standard deviation
>> > of ydata, as I expected."  Today I independently came to the same
>> > conclusion.
>> >
>> > This thread generated some discussion but seemingly no agreement that
>> > the covariance output of `curve_fit` is not what would be expected.  I
>> > think the discussion wasn't as focused as possible because the example
>> > was too complicated.  With that I provide here about the simplest
>> > possible example, which is fitting a constant to a constant dataset,
>> > aka computing the mean and error on the mean.  Since we know the
>> > answers we can compare the output of `curve_fit`.
>> >
>> > To illustrate things more easily I put the examples into an IPython
>> > notebook which is available at:
>> >
>> >   http://nbviewer.ipython.org/5014170/
>> >
>> > This was run using scipy 0.11.0 by the way.  Any further discussion on
>> > this topic to come to an understanding of the covariance output from
>> > `curve_fit` would be appreciated.
>> >
>> > Thanks,
>> > Tom
>> > _______________________________________________
>>
>> chi2 = np.sum(((yn-const(x, *popt))/sigma)**2)
>> perr = np.sqrt(np.diag(pcov)/(chi2/(x.shape[0]-1)))
>>
>> Perr is then the actual error in the fit parameter. No?
>>
>> -Eric
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>
>
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