[Ifeffit] S02-Interpretation

[Matt Newville]

Hi Shelly,

On Thu, 15 Apr 2004, Kelly, Shelly D. wrote:

> Hi Matt
> 
> > > Now, if I have two samples and determined the S02 value according to
> > > the way which Bruce has in his supplement to the FEFFIT course, 
> > 
> > How do you mean this?  Is this the 'plot three curves of sigma2 v.  
> > S02 curves for three different k-weights' again?  I find this 
> > approach puzzling and dangerous.  I do not understand why the slope
> > (correlation) of sigma2 v. S02 should depend on k-weight in 
> > any systematic way -- does anyone else know why it should??  
> > What you want is the S02 and sigma2 that gives the lowest 
> > chi-square, not where these lines cross.
> 
> I have found that usually there is a "larger than one would like"
> correlation between the amplitude and phase terms in the EXAFS equation.
> But the different terms have different k-dependencies.  Low k-weights
> will give more weight to an accurate E0, whereas higher k-weights will
> give a more accurate deltar.  Although the errors will be large.  
> 
> If you plot the dependence of these variables on the k-weight, or better
> yet use all three k-weights in the fit, you will find that the best-fit
> value is consistent with the one k-weight value but that the uncertainty
> is lower because you are distinguishing between the two coorelated
> variables by including the k-dependence in the fit.

Sure, I agree with all that, and would gladly echo you that the
phase and amplitude are mostly, but not completely separated.

Getting more accurate E0 and S02 with lower k weighting and deltaR
and sigma2 with higher k weighting is consistent with Bruce's
k-weight plot and the figures you sent me too: at higher k-weight,
sigma2 is less dependent on S02.  This all seems perfectly
reasonable, and makes sense since chi(k) depends on E0 as k^-1, on
S02 as k^0, on deltar as k^1, and on sigma2 as k^2.  And this is why
using multiple k-weights works to lower the correlations between E0
and detlaR and between sigma2 and S02.  I'm just not sure I
completely understand how systematic and universal the dependence on
k-weight is.  Like, the change in correlation/slope might depend on
back-scattering species and/or k-ranges as much as k-weight.  I 
haven't thought about this in any detail -- has anyone else?

Anyway, my main complaint is (or was meant to be) not with using any
systematic dependence of the correlations on k-weight (fitting with
multiple-k-weights is highly recommended!!!) but with the
line-crossing trick itself.  If I understand right, these lines
don't include the value of chi-square, and it's not obvious to me
that the lines have to cross where chi-square is smallest.  OTOH, it
seems that many other have used this trick successfully, so maybe
I'm missing something: is the experience that the lines always cross
where chi-square is smallest?

To me, doing the multiple k-weight fit seems much easier and more
robust, but maybe there's something else going on that I don't 
understand.

--Matt