[Ifeffit] Question about transform windows and statistical parameters

[Scott Calvin]

Hi Brandon,

I don't find this terribly surprising.

First, a little background which you may or may not know:

Reduced chi-square is a statistical parameter which requires a  
knowledge of the uncertainty of the measurement to compute. In theory,  
therefore, it "knows" that a "good" fit to noisy data will not be as  
close in an absolute sense as a "good" fit to high-quality data.

The problem, however, is that it's difficult to know what is the  
proper quantity to use for the uncertainty of the measurement in EXAFS  
analysis. One could use the standard deviation of subsequent scans,  
but that is only sensitive to random scan-to-scan error. Something  
like, say, a monochromator glitch is quite reproducible, and yet most  
of us would consider it to be part of the measurement error.

So the default behavior of Ifeffit is to look at the Fourier transform  
between 15 and 25 angstroms, and figure that any amplitude there is  
due to error of some kind, and not signal. It then makes the  
assumption that the same amount of error is present in the range being  
fit (i.e. the error is "white"), and from there computes the reduced  
chi-square.

This is in some sense a dubious procedure, but the real problem is  
that we don't have a good method for estimating the measurement  
uncertainty, so we have to do something.

As long as we are comparing fits to exactly the same data, on the same  
k-range, with the same k-weight, with the same windows, then changes  
in reduced chi-square are worth looking at. If all you've done is  
change a constraint or change the R-range being fit, for instance, a  
lower reduced chi-square is a good sign (use the Hamilton test if you  
want to be rigorous about it.)

But change the k-range, or the k-weight, or the window, or the data,  
and Ifeffit's estimate of the uncertainty can change wildly, causing a  
correspondingly wild change in reduced chi-square. After all, one  
glitch toward the end of the k-range you are thinking can introduce a  
lot of high-R amplitude in to the Fourier transform, and different  
windows would treat it very differently. But single-point glitches  
often don't have much effect on the results of your fit, precisely  
because they do affect the high-R part of the Fourier transform much  
more than low-R part.

Ifeffit's default behavior can be overridden, if you so choose. The  
parameter "epsilon" (available on the Data panel of Artemis) overrides  
Ifeffit's usual estimate for uncertainty. So in your case, I suggest  
putting a number--any number--in for epsilon, and then comparing fits  
using the two windows. Probably you will find that the reduced chi- 
squares become much more similar to each other.

Incidentally, while in this case the default behavior of Ifeffit is  
merely distracting, there is a circumstance where it can be a more  
substantial problem: mutliple data-set fits (e.g. on multiple edges of  
the same sample). If Ifeffit finds uncertainties for the different  
data sets that are quite different from each other because, for  
instance, of the presence of a glitch in one, it will in effect weight  
the data very differently when doing a fit.  In multiple-data set  
fits, therefore, it is often advisable to come up with your own scheme  
for setting epsilons (perhaps inversely proportional to the edge jump  
of the set, or something like that), to avoid wonky weightings.

--Scott Calvin
Sarah Lawrence College


On May 11, 2011, at 12:47 PM, Brandon Reese wrote:

> Hello everybody,
>
> I am working on fitting some EXAFS of amorphous materials and have  
> noticed an odd (in my mind) behavior when changing transform  
> windows.  I settled on a fit using all three k-weights and the  
> Hanning transform window obtaining statistical parameters of  
> R=0.0018 and chi_R=361.  I decided to change the transform window to  
> a Kaiser-Bessel to see what would happen.  The refined parameters  
> came out more or less the same, well within the error bars, with the  
> Hanning windows having slightly smaller error bars.  But my  
> statistical parameters changed significantly to R=0.0022 and  
> chi_R=89.354.  It seems that this large change may be related to why  
> we can't use the chi_R parameter to compare fits over different k- 
> ranges, but I am not sure about that.  Have other people seen this?   
> I would guess it means that when looking for trends in different  
> data sets, it is more important to be consistent, rather than which  
> specific window type is used.
>
> Thanks,
> Brandon
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