[Ifeffit] What confidence limit is implied in the errorbars forleast-squares fitting in Athena

[Kelly, Shelly]

Hi Don,

I'll try to be more explicit. Species for me means the local
stereochemical atomic environment of some atom. The XANES spectra from
Species A (A is some specific species) may or may not be unique.  It
surely isn't 100% unique (orthogonal) from all other species, meaning
that you can likely make a XANES spectrum of Species A by using a
combination of XANES spectra from other species. Let us pretend 50% B,
40% C, 8% D.  Just to be fair let's pretend that you have a 2% misfit
since Species A XANES spectra is a bit unique. Then pretend that your
sample is actually a combination of 50% Species A and 50% Species A'.
And species A' can be made to closely resemble 50% B and 50% C, more or
less exactly.  

Then if you happen to have the standard spectra from A and A', then a
50/50 combination will work the best since A is a bit unique. But a fit
using 50% A and 25%B and 25%C will work just as well. If you don't have
A but you do have A' then 96% A' (giving 50% B and 50% C) and 4% D with
a bit of misfit will work well or if you don't have A or A' but you have
B,C and D then you might say 50%B, 45%C and 5%D is the answer when it
really isn't the answer at all.

Just to be fair, species B and C are likely related to species A and A'
such that the endeavor is still worth while. But you will do the
community justice by ASSUMING that you have B and C and D rather than A
and A', since that is way more likely the case.

My suggestions are (1) always look in the literature and see how much
the XANES spectra change for different species. (2) Measure as many
standards as possible.  (3) Use the chemistry and other knowledge you
have about the system. (4) Be aware of the problem and don't overstate
your conclusions. You make assumptions about the species in your sample
when you make LCF and so state your results in the context of those
assumptions. These assumptions are likely the biggest source of
uncertainty and way bigger than a few percent.

Shelly


-----Original Message-----
From: ifeffit-bounces at millenia.cars.aps.anl.gov
[mailto:ifeffit-bounces at millenia.cars.aps.anl.gov] On Behalf Of Don R
Baker
Sent: Thursday, October 02, 2008 7:26 PM
To: XAFS Analysis using Ifeffit
Subject: Re: [Ifeffit] What confidence limit is implied in the errorbars
forleast-squares fitting in Athena

Hi Shelly,

I am very interested in Andrew's question too, but I am to ignorant to
fully understand your response.  Could you please provide some more
detail?  For example, when you state "a large source of uncertainty can
come from the representation of the standards in matching the species in
the sample." do you mean that heterogeneities (as Bruce mentioned in his
email) in the standards are propagated into the fits of the unknowns?
Or instead do you mean that an inappropriate choice of standards can
create unreliability in the fit?  I would appreciate any details you can
add to your repsonse.

Thanks,

Don

On Thu, 2008-02-10 at 14:22 -0700, Kelly, Shelly wrote:
> Hi Andrew,
> 
>  
> 
> If you are fitting XANES spectra with standards, a large source of
> uncertainty can come from the representation of the standards in
> matching the species in the sample.
> 
>  
> 
> Shelly
> 
>  
> 
> 
> ______________________________________________________________________
> 
> From: ifeffit-bounces at millenia.cars.aps.anl.gov
> [mailto:ifeffit-bounces at millenia.cars.aps.anl.gov] On Behalf Of Andrew
> Sent: Thursday, October 02, 2008 3:49 PM
> To: ifeffit at millenia.cars.aps.anl.gov
> Subject: [Ifeffit] What confidence limit is implied in the error bars
> forleast-squares fitting in Athena
> 
>  
> 
> Hi everyone,
> 
>  
> 
> I'm fitting data with the least-squares method in Athena and am not
> sure what the error bars correspond to. What I mean, are these 95%
> confidence limits, or is it some other statistical way for error
> analysis?  If Athena says the weight of one phase is 0.049 (0.003),
> what confidence are in the 0.003 error bar reported by Athena?
> 
>  
> 
> (I have done a PCA of the XANES, and XRDs of the samples and am pretty
> confident in the phases that I'm fitting).
> 
>  
> 
> I greatly appreciate the help!
> 
>  
> 
> Andrew Campos
> 
> _______________________________________________
> Ifeffit mailing list
> Ifeffit at millenia.cars.aps.anl.gov
> http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
-- 
Melting rocks today for a better tomorrow . . .
Don R. Baker, Professor of Geochemistry, Earth and Planetary Sciences,
McGill University, Montreal, QC CANADA  phone: 1-514-398-7485


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