[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
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

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:


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.


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