[SciPy-User] Revisit Unexpected covariance matrix from scipy.optimize.curve_fit
Tom Aldcroft
aldcroft@head.cfa.harvard....
Fri Feb 22 09:41:59 CST 2013
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
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