[Ifeffit] Breaking down correlationships between parameters

[Matt Newville]

HI Jatin,


On Sat, Mar 21, 2015 at 8:06 AM, Rana, Jatinkumar Kantilal <
jatinkumar.rana at helmholtz-berlin.de> wrote:

>  Dear All,
>
>  I have stumbled upon a question regarding correlationships between
> various parameters in EXAFS fitting. As we know, the parameters S02*N and
> sigma2 are highly correlated (where N is the number of nearest neighbors).
>
>  I would like to determine the number of nearest neighbors for a series
> of sample subjected to some treatment. I can do this by simply setting S02
> to a value for a given absorber (based on the literature or my own
> measurements of some reference compounds) and letting N and sigma2 vary in
> a fit. However, the problem is the physical process which changes the
> number of nearest neighbors, also introduces structural disorder in
> samples. Thus, I always get the values of N overestimated due to its
> correlationship with sigma2.
>
>
By itself, the size of the correlation between any 2 variables should not
bias the best-fit results.  So, the high correlation of N and sigma2 should
not always overestimate N.   If you're consistently seeing N overestimated,
it is probably not because sigma2 is also overestimated, but more likely to
be due to some other reason.  Like, if N is consistently too high, perhaps
S02 is set artificially low.


>  I know of a method which can be used to breakdown the correlationship
> between S02 and sigma2 by setting a series of S02 values at different
> k-weights and refining the corresponding sigma2 as discussed in several
> literature. However, in this approach the explicit assumption is, S02 is
> the property of absorbing atoms and thus is independent of changes
> occurring inside the sample. In my case, however, both sigma2 and N vary
> with changes inside samples. Is there any way to break this
> correlationship ?
>
>
The idea of setting N*S02 and using different k-weights is sort cheating.
By setting N*S02 you're purposely ignoring the correlation.     Using
multiple k-weights in a fit can lower the correlation on N*S02 and sigma2
somewhat, but it certainly does not break it.   I've not seen a case where
it makes a substantial reduction (say, below 0.5, and rarely below 0.75).
That is, if you just check using a k-weight of 1,2, and 3 in Artemis,
you'll likely see the correlation drop from something like 0.95 to 0.90 in
the best cases -- hardly "breaking the correlation".    Extending the
k-range as much as possible (including to low-k) can also reduce the
correlation, but again, only by small amounts.   Like that for R and E0,
N*S02 and sigma2 will be highly correlated even if you measure EXAFS to
very high k and fit   The correlation is basically endemic.

But, correlation does not imply a bias.  It can *allow* some bias to skew
the results substantially, and increases the uncertainties in these values,
but it is really not the ultimate cause of the results.

--Matt
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