[SciPy-user] curve_fit failure when supplying uncertainties

[ElMickerino]

Great, thanks so much for your help.  I seem to recall that empty bins
require special handling when fitting histograms, so this makes sense.  I
was using variance of the bin content, which are assumed to poisson
distributed (ie. if bin 'i' has content N_i, then var(bin_i) = sqrt(N_i) ). 
This works fine for large N, but I believe that asymmetric errors must be
used for small bin content.

Is there a convenient way of supplying asymmetric errors to a least square
fit in scipy?

Thanks again,
Michael


josef.pktd wrote:
> 
> 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
>> Sent from the Scipy-User mailing list archive at Nabble.com.
>>
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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
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> 
> 

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