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

massimo sandal massimo.sandal@unibo...
Wed Nov 12 09:36:31 CST 2008

Bruce Southey wrote:
> You also have a very bad fit as the standard errors are huge relative to 
> the estimate meaning your parameters are not statistically different 
> from zero. 

Huh, why?
Parameters: 4.90666526e+06   4.78090340e+09
Scaled error bars: 6.99319913e+04   6.68959208e+08

It seems values are estimated with roughly 1% and 10% confidence, 
respectively. Am I wrong?

> Physics is one thing but the data tell a very different story 
> perhaps due to measurement errors. 

The data are right.

> The linear regression of x on y gives 
> a residual variance of  2.86121E-22 and R-squared is 73% (approx 73% for 
> the model above). I don't see any evidence for a nonlinear fit 
> especially if you bother to plot the data. As I previously said, you 
> probably would get a better fit using splines or similar because of the 
> variability present.

I am probably bad at communicating, so I repeat.

This is a SECTION of the data. A tiny SECTION of a 2048-point force 
curve. Being a small section, it is not surprising it is almost linear.
I just posted that bunch of points because they fitted correctly with 
the equation and it was totally pointless to copy and paste hundreds of 
numbers just to make people sleep happily about my own data.

Each peak in the force curve is clearly non linear, and I posted 
examples of what I mean. If you want, you can download the software from 
http://code.google.com/p/hooke and I can send you examples of whole 
relevant data, fresh from the instrument.

I am not trying to fit the data with whatever model works best. I *want 
to pick up well defined parameters* from a physical model.
If you have doubts on the physical consistency of the model or on its 
application to my data, you're welcome to come here and discuss with me 
and my coworkers (among them physicists).

Thanks for your interest, but really, you are misunderstanding the 
issue. If you want information on single molecule force spectroscopy of 
polymers, I can give you some reference.

Thanks for the bibliography too!

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

snail mail:
Via Irnerio 48, 40126 Bologna, Italy



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