[SciPy-user] curve_fit failure when supplying uncertainties

[josef.pktd at gmail.com]

On Sat, Mar 7, 2009 at 7:18 PM, ElMickerino <elmickerino at hotmail.com> wrote:
>
> I think I've identified a problem with curve_fit which occurs when one
> attempts to fit normally distributed data with a gaussian.  From the
> documentation of curve_fit, it appears that 'sigma' should be the
> uncertainties on the y-values of the data; however, the following example
> (see attached code) should make it clear that there's a problem with this.
>
> My best guess is that the sigma are actually weights (=1.0/sigma).  Can
> anyone confirm or deny this?  Seems like from the name it should be
> uncertainties but from the behavior of the code it appears otherwise.
>
> Also, I was wondering if there's a way to supply asymmetric errors to
> curve_fit (or for that matter, to leastsqr or any wrapper thereof).
>
> Thanks very much,
> Michael
>
> http://www.nabble.com/file/p22380378/testFit.py testFit.py
> --
> View this message in context: http://www.nabble.com/curve_fit-failure-when-supplying-uncertainties-tp22380378p22380378.html
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>
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sigma is the vector of standard deviations for the observations. The
weights in the least squares objective function are 1/sigma.
Essentially it is a heteroscedastic non-linear generalized least
squares estimation.

In your case err contains zeros, which means the variance is zero and
the weight 1/sigma for these observations would be infinite. curve_fit
cannot handle zero standard deviation. Infinite standard deviation
works because then the weight becomes zero.

If you force your err to be strictly positive, then this works, e.g.

>>> curve_fit(gaus, centers, data, sigma=1e-6+err)
(array([  1.91520894e+03,   1.68957830e-01,   6.19128687e-01]),
array([[  3.03590409e-09,   5.11571694e-18,  -6.69243949e-18],
       [  5.11571694e-18,   4.43479563e-16,   6.18126633e-17],
       [ -6.69243949e-18,   6.18126633e-17,   3.02641036e-17]]))


I haven't looked closely at the rest of your file, so I'm not sure
about the interpretation of your err

Josef