[SciPy-User] optimize.leastsq error estimation

Joe Philip Ninan indiajoe@gmail....
Thu Mar 21 15:10:30 CDT 2013


Hi,
I want to confirm whether i understood the documentation of
optimize.leastsq correctly.
(
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.html)
For estimating the error in the fitted parameter.
The documentation says :
"This matrix (cov_x) must be multiplied by the residual variance to get the
covariance of the parameter estimates"
i.e. Multiply the output cov_x with the "reduced chi square". Right? and
take sqrt of corresponding diagonal element from covariance matrix.
Where "residual chi square" is the sum of {[(fitted function -
data)/sigma]**2} /N
and where N is degrees of freedom [= len(data)-number of parameters]
And sigma is the error in each data point.

I mainly want to confirm whether the divide by sigma is required or not.
(I couldn't find the definition of "residual variance" in documentation, so
i assumed it is reduced chi square).

Thanking you,
Joe


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