[SciPy-user] scipy.optimize.leastsq and covariance matrix meaning

[massimo sandal]

Hi,

I have a trouble with the covariance matrix in the output of 
scipy.optimize.leastsq . I am trying to find the estimated sigma of the 
parameters obtained by the fit. Please bear with me since my statistics 
knowledge is poor. I understand that the diagonal of the covariance 
matrix should return me the variance values of each parameter.

Problems are:
1) The variance of such parameters look unreasonably large to me, 
despite the fact I obtain an *excellent* fit over a lot of data points 
(and values extremly well coherent with expected).
2) The non-diagonal values of the covariance are also unreasonably 
large, which lets me doubt that picking simply the diagonal values is 
the correct thing to do.

The residuals function is:

         def residuals(params,y,x,T):
             '''
             Calculates the residuals of the fit
             '''
             lambd, pii=params

             Kb=(1.38065e-23)
             therm=Kb*T

             err = y-( (therm*pii/4) * (((1-(x*lambd))**-2) - 1 + 
(4*x*lambd)) )

             return err

For example, a common entity of values is:
4390808.6184609979
3993219683.7749424

and the relative covariance matrix is
[[  1.97019986e+29  -2.67163157e+33]
  [ -2.67163157e+33   3.78415451e+37]]

...which concerns me.

m.
-- 
Massimo Sandal , Ph.D.
University of Bologna
Department of Biochemistry "G.Moruzzi"

snail mail:
Via Irnerio 48, 40126 Bologna, Italy

email:
massimo.sandal at unibo.it

web:
http://www.biocfarm.unibo.it/samori/people/sandal.html

tel: +39-051-2094388
fax: +39-051-2094387
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