Re: [Ifeffit] Breaking down correlationships between parameters

23 Mar 2015

      Hi Scott,

Thanks for your explanation. It means the reverse can also be true, i.e., I can guess N1 (nearest-neighbors in the first shell) and S02 by setting N2, N3 and N4 to values known from other analysis. I did a quick check by fitting the data.

I conducted two fits:
1) setting S02 and guessing only N1
2) guessing both N1 and S02.

To my surprise, both the fits gave very similar results, except that the fit#1 refined value of N1 to a higher side, while fit#2 estimated N1 closer to a physically reasonable value (as expected).

I always constrained S02 when refining N for any path, due to 100% correlation between them. However, I am surprised to know that they can be refined independently.

Best regards,
Jatin

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Today's Topics:

   1. Re: Breaking down correlationships between parameters
      (Scott Calvin)

----------------------------------------------------------------------

Message: 1
Date: Mon, 23 Mar 2015 09:18:21 -0400
From: Scott Calvin 
To: XAFS Analysis using Ifeffit 
Subject: Re: [Ifeffit] Breaking down correlationships between
	parameters
Message-ID: <78C1636C-91CF-4C8C-9D48-3EC361BB7237@slc.edu>
Content-Type: text/plain; charset="utf-8"

Hi Jatin,

The key is that S02 should be the same for all paths.

For example:

Suppose you are very confident path 1 has a coordination number of 6, because of prior knowledge you have about the system. Paths 2, 3, and 4 have unknown coordination numbers, however.

N1 (i.e. the degeneracy of path 1) you set to 6.

You guess S02, N2, N3, and N4. Of course, the way Artemis and Ifeffit implement that, you're writing N1*S02 for the S02 field of Path 1, N2*S02 for the S02 field of Path 2, etc., and then setting N1 = 6 and guessing S02, N2, N3, and N4.

There is now enough information for S02, N2, N3, and N4 to each be fitted without 100% correlation.

?Scott Calvin
Sarah Lawrence College
...
On Mar 23, 2015, at 8:54 AM, Rana, Jatinkumar Kantilal  wrote:
Hi Chris,
The term N*S02 is fitted for each path of the FEFF calculation. So my question is, even if we know N with a great certainty for some path, how can we vary both N and S02 for other paths ? or Did I understand it wrong ?
Best regards,
Jatin
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Today's Topics:
1. Re: Breaking down correlationships between parameters
     (Rana, Jatinkumar Kantilal)
  2. Re: Breaking down correlationships between parameters
     (Chris Patridge)
----------------------------------------------------------------------
Message: 1
Date: Mon, 23 Mar 2015 11:00:19 +0000
From: "Rana, Jatinkumar Kantilal"

To: "ifeffit@millenia.cars.aps.anl.gov"

Subject: Re: [Ifeffit] Breaking down correlationships between
       parameters
Message-ID: 
Content-Type: text/plain; charset="utf-8"
Hi Scott,
Thank you for your comments. Can you please elaborate a little bit more on this "In cases like that, both N for all paths but one and S02 can be fit without 100% correlation."
Best regards,
Jatin
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ifeffit-request@millenia.cars.aps.anl.gov
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Today's Topics:
1. Re: Breaking down correlationships between parameters
     (Scott Calvin)
  2. Re: Breaking down correlationships between parameters
     (Matt Newville)
  3. Re: Breaking down correlationships between parameters
     (Rana, Jatinkumar Kantilal)
----------------------------------------------------------------------
Message: 1
Date: Sun, 22 Mar 2015 13:44:28 -0400
From: Scott Calvin 
To: XAFS Analysis using Ifeffit 
Subject: Re: [Ifeffit] Breaking down correlationships between
       parameters
Message-ID: 
Content-Type: text/plain; charset="utf-8"
One side-comment from me:
On Mar 22, 2015, at 12:52 PM, Matt Newville mailto:newville@cars.uchicago.edu> wrote:
N and S02 are always 100% correlated (mathematically, not merely by the finite k range).
Matt is saying that N and S02 are always 100% correlated for a single path. But in some situations you might know N for one path but not others. For example, you might know that the absorbing atom is octahedrally coordinated to oxygen but not be as certain as to next-nearest neighbors, or that there are copper atoms on the corners of a simple cubic lattice with a mixture of atoms at other positions. In cases like that, both N for all paths but one and S02 can be fit without 100% correlation.
The degeneracy of multiple-scattering paths can often be constrained in terms of the coordination numbers for direct-scattering paths, which can further reduce (not ?break?) the correlation.
In terms of the main question, I agree with Matt: I don?t think there?s much point in using the line-crossing technique nowadays; fitting using multiple k-weights simultaneously accomplishes the same thing but is a bit easier to interpret statistically.
?Scott Calvin
Sarah Lawrence College
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Message: 2
Date: Sun, 22 Mar 2015 15:56:20 -0500
From: Matt Newville 
To: XAFS Analysis using Ifeffit 
Subject: Re: [Ifeffit] Breaking down correlationships between
       parameters
Message-ID:

Content-Type: text/plain; charset="utf-8"
On Sun, Mar 22, 2015 at 12:44 PM, Scott Calvin

wrote:
...
One side-comment from me:
On Mar 22, 2015, at 12:52 PM, Matt Newville

wrote:
N and S02 are always 100% correlated (mathematically, not merely by
the finite k range).
Matt is saying that N and S02 are always 100% correlated *for a
single path*. But in some situations you might know N for one path
but not others. For example, you might know that the absorbing atom
is octahedrally coordinated to oxygen but not be as certain as to
next-nearest neighbors, or that there are copper atoms on the corners
of a simple cubic lattice with a mixture of atoms at other positions.
In cases like that, both N for all paths but one and S02 can be fit without 100% correlation.
Yes, I completely agree with Scott -- this is a good point that I
neglected.   In addition to looking at multiple shells, one might also
consider using temperature or pressure dependence to separate N*S02 and
sigma2.   Those aren't without assumptions, and still don't remove the
inherent correlation, but are useful approaches.
The degeneracy of multiple-scattering paths can often be constrained
in
...
terms of the coordination numbers for direct-scattering paths, which
can further reduce (not ?break?) the correlation.
In terms of the main question, I agree with Matt: I don?t think
there?s much point in using the line-crossing technique nowadays;
fitting using multiple k-weights simultaneously accomplishes the same
thing but is a bit easier to interpret statistically.
?Scott Calvin
Sarah Lawrence College
_______________________________________________
Ifeffit mailing list
Ifeffit@millenia.cars.aps.anl.gov
http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
--Matt
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Message: 3
Date: Mon, 23 Mar 2015 09:16:02 +0000
From: "Rana, Jatinkumar Kantilal"

To: "ifeffit@millenia.cars.aps.anl.gov"

Subject: Re: [Ifeffit] Breaking down correlationships between
       parameters
Message-ID: 
Content-Type: text/plain; charset="utf-8"
Hi Matt,
Thank you very much for your detailed explanation. As you pointed out that this approach ignores the statistical significance of fits and assumes that all fits are "good" fits. Also, the point that this approach yields a value of the parameter which is only slightly less correlated with the other one, but not completely removes the correlation. It makes it really clear to me that how this approach works and what are the pros and cons.
Well, I myself has never tried this approach of minimizing the correlation between N*S02 and sigma2, but I read a lot about it in the literature. With my limited knowledge about the method, I could not judge this approach, although I had my own doubts.
I truly appreciate your efforts in providing me a deeper insight into this approach.
Best regards,
Jatin
-----Original Message-----
From: ifeffit-bounces@millenia.cars.aps.anl.gov
[mailto:ifeffit-bounces@millenia.cars.aps.anl.gov] On Behalf Of
ifeffit-request@millenia.cars.aps.anl.gov
Sent: 22 March, 2015 18:00
To: ifeffit@millenia.cars.aps.anl.gov
Subject: Ifeffit Digest, Vol 145, Issue 40
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1. Re: Breaking down correlationships between parameters
     (Matt Newville)
----------------------------------------------------------------------
Message: 1
Date: Sun, 22 Mar 2015 11:52:30 -0500
From: Matt Newville 
To: XAFS Analysis using Ifeffit 
Subject: Re: [Ifeffit] Breaking down correlationships between
       parameters
Message-ID:

Content-Type: text/plain; charset="utf-8"
Hi Jatin,
On Sat, Mar 21, 2015 at 10:41 AM, Rana, Jatinkumar Kantilal < jatinkumar.rana@helmholtz-berlin.de> wrote:
...
Hi Matt,
Thanks a lot for your prompt reply. The method I am referring to is
not the multiple k-weight fits by constraining N*S02. My apologies
for not being clear enough. Let's do it again. I am actually
referring to an approach where we take an advantage of a different
k-dependence of various parameters to breakdown correlations between
them. For example, S02 and sigma2. S02 is k-independent and Sigma2 has k^2 dependence.
Yes, I am familiar with this approach, and I understand that this is what you are using.  What I am saying is that this does not work nearly as well as (sometimes) claimed, and is sort of cheating.  It ignores the measures of statistical significance.
In this case, to breakdown correlation between S02 and sigma2,
The correlation between N*S02 and sigma2 is inherent to the finite k-range of the EXAFS signal.  It cannot be "broken", though it might be reduced.
...
one can assume a series of S02 values and perform fits using a single
k-weight each time (say k-weight 1,2 and 3) and record corresponding
sigma2 values.
Let us say for k-weight =1, a series of preset S02 values will result
in a
...
series of corresponding sigma2 values refined in fits, which can be
plotted as a straight line in sigma2 vs. S02 plot.
OK, one can fit sigma2 with a series of preset values on N*S02.  That's fine.  But it does NOT lead to an infinitely thin line of sigma2 vs.
N*S02.  Each sigma2 value on that line has a width, corresponding to its
uncertainty.   In fact, the line you produce nicely demonstrates and
measures the correlation of N*S02 and sigma2 as the slope of this line.
...
Similar straight lines can be obtained for fits using k-weight = 2
and then 3.
Now, these three lines may intersect at or near some point, which will
...
determine the "true" value of parameters independent of k-weight.
The different lines (each with finite thickness) will give a *range of
values* for N*S02 and sigma2, not a single value.
The biggest problem with this approach is that it ignores the relative goodness-of-fits (let's just assume that is 'chi-square' for the purpose of
this discussion) for the fits along these lines.   Some fits are better
than others, and this approach completely ignores that fact, and equally importantly ignores the fact that there is a range of values for chi-square
that are consistent with "good".     If you include these values, your
linear plot will become contours of chi-square as a function of N*S02 and
sigma2.   And, yes, by using different k-weights and k-ranges and so on you
can get overlapping contour plots which may reduce the correlation a small amount when looked at as an ensemble.  And you can find a best set of values for N*S02 and sigma2, but *each* of these will have an uncertainty.
So, you can use this approach to find a good value for N*S02, but it is not breaking the correlation.  You can do this by hand.  Or you can just do a
fit with datasets with different k-weights and k-ranges.   When you do this
as a fit, you will see that the correlation is still fairly large.
Also, just to be clear, this is absolutely not a "true" value.  It is a measured value.  Not at all the same thing.
One can then constrain S02 to a value obtained from the point of
...
intersection of three lines and vary sigma2 in a fit.
Well, one can certainly set N*S02 to some value and fit sigma2.  As I said earlier, this ignores the correlation of N*S02 and sigma2, but does not remove that correlation.
...
In this particular case, however, the advantage is, S02 does not
depend on changes inside sample and we have very good estimate of its
range (say 0.7
- 1.0).
Now suppose instead of S02 (which i now set to a reasonable value), I
am interested in determining N, but it is highly correlated with
sigma2. Each time when disorder in the sample increases, the sigma2
increases and due to its high correlation, N is also overestimated.
On the other hand, when the disorder in the sample decreases, the
sigma2 decreases and I can have a "true" estimation of N in the
sample. Can I still apply the above mentioned approach to break the correlationship between N and sigma2 and get a "true"
estimation of N, even if disorder is high in my samples ? or it is
simply not possible due to the fact that both N and sigma2 varies
with changes inside the sample.
N and S02 are always 100% correlated (mathematically, not merely by the finite k range).  So, to the extent that the approach works at all, you can use it for "N" or "S02".  Really, the approach is comparing N*S02 and sigma2, in one case you asserted a value of "N" and projected all changes to "S02" -- you can equally assert "S02" and project all changes to "N".
To be clear,  this is not going to find the "true" value of anything, because no analysis is ever going to find the "true" value -- it's going to find a measured value.
Finally, the correlation of N*S02 and sigma2 does not imply a bias in the values for N*S02.  N*S02 is NOT overestimated because it is highly correlated with sigma2.
Hope that helps,
--Matt
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Mitglied der Hermann von Helmholtz-Gemeinschaft Deutscher Forschungszentren e.V.
Aufsichtsrat: Vorsitzender Prof. Dr. Dr. h.c. mult. Joachim Treusch,
stv. Vorsitzende Dr. Beatrix Vierkorn-Rudolph
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Postadresse:
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------------------------------
Message: 2
Date: Mon, 23 Mar 2015 07:15:05 -0400
From: Chris Patridge 
To: XAFS Analysis using Ifeffit 
Subject: Re: [Ifeffit] Breaking down correlationships between
       parameters
Message-ID: <29942DF9-8043-424E-BDCC-9CA19EB4AC9B@buffalo.edu>
Content-Type: text/plain;       charset=utf-8
I think Scott was pointing out that first neighbors may be known with high certainty and therefore you can set this value thereby removing it and slightly reducing the correlations.
Chris
Sent from my iPhone
...
On Mar 23, 2015, at 7:00 AM, Rana, Jatinkumar Kantilal  wrote:
Hi Scott,
Thank you for your comments. Can you please elaborate a little bit more on this "In cases like that, both N for all paths but one and S02 can be fit without 100% correlation."
Best regards,
Jatin
-----Original Message-----
From: ifeffit-bounces@millenia.cars.aps.anl.gov
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ifeffit-request@millenia.cars.aps.anl.gov
Sent: 23 March, 2015 10:16
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Today's Topics:
1. Re: Breaking down correlationships between parameters
    (Scott Calvin)
 2. Re: Breaking down correlationships between parameters
    (Matt Newville)
 3. Re: Breaking down correlationships between parameters
    (Rana, Jatinkumar Kantilal)
---------------------------------------------------------------------
-
Message: 1
Date: Sun, 22 Mar 2015 13:44:28 -0400
From: Scott Calvin 
To: XAFS Analysis using Ifeffit 
Subject: Re: [Ifeffit] Breaking down correlationships between
      parameters
Message-ID: 
Content-Type: text/plain; charset="utf-8"
One side-comment from me:
On Mar 22, 2015, at 12:52 PM, Matt Newville mailto:newville@cars.uchicago.edu> wrote:
N and S02 are always 100% correlated (mathematically, not merely by the finite k range).
Matt is saying that N and S02 are always 100% correlated for a single path. But in some situations you might know N for one path but not others. For example, you might know that the absorbing atom is octahedrally coordinated to oxygen but not be as certain as to next-nearest neighbors, or that there are copper atoms on the corners of a simple cubic lattice with a mixture of atoms at other positions. In cases like that, both N for all paths but one and S02 can be fit without 100% correlation.
The degeneracy of multiple-scattering paths can often be constrained in terms of the coordination numbers for direct-scattering paths, which can further reduce (not ?break?) the correlation.
In terms of the main question, I agree with Matt: I don?t think there?s much point in using the line-crossing technique nowadays; fitting using multiple k-weights simultaneously accomplishes the same thing but is a bit easier to interpret statistically.
?Scott Calvin
Sarah Lawrence College
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Message: 2
Date: Sun, 22 Mar 2015 15:56:20 -0500
From: Matt Newville 
To: XAFS Analysis using Ifeffit 
Subject: Re: [Ifeffit] Breaking down correlationships between
      parameters
Message-ID:

Content-Type: text/plain; charset="utf-8"
On Sun, Mar 22, 2015 at 12:44 PM, Scott Calvin

wrote:
...
One side-comment from me:
On Mar 22, 2015, at 12:52 PM, Matt Newville

wrote:
N and S02 are always 100% correlated (mathematically, not merely by
the finite k range).
Matt is saying that N and S02 are always 100% correlated *for a
single path*. But in some situations you might know N for one path
but not others. For example, you might know that the absorbing atom
is octahedrally coordinated to oxygen but not be as certain as to
next-nearest neighbors, or that there are copper atoms on the
corners of a simple cubic lattice with a mixture of atoms at other positions.
In cases like that, both N for all paths but one and S02 can be fit without 100% correlation.
Yes, I completely agree with Scott -- this is a good point that I
neglected.   In addition to looking at multiple shells, one might also
consider using temperature or pressure dependence to separate N*S02 and
sigma2.   Those aren't without assumptions, and still don't remove the
inherent correlation, but are useful approaches.
The degeneracy of multiple-scattering paths can often be constrained
in
...
terms of the coordination numbers for direct-scattering paths, which
can further reduce (not ?break?) the correlation.
In terms of the main question, I agree with Matt: I don?t think
there?s much point in using the line-crossing technique nowadays;
fitting using multiple k-weights simultaneously accomplishes the
same thing but is a bit easier to interpret statistically.
?Scott Calvin
Sarah Lawrence College
_______________________________________________
Ifeffit mailing list
Ifeffit@millenia.cars.aps.anl.gov
http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
--Matt
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Message: 3
Date: Mon, 23 Mar 2015 09:16:02 +0000
From: "Rana, Jatinkumar Kantilal"

To: "ifeffit@millenia.cars.aps.anl.gov"

Subject: Re: [Ifeffit] Breaking down correlationships between
      parameters
Message-ID: 
Content-Type: text/plain; charset="utf-8"
Hi Matt,
Thank you very much for your detailed explanation. As you pointed out that this approach ignores the statistical significance of fits and assumes that all fits are "good" fits. Also, the point that this approach yields a value of the parameter which is only slightly less correlated with the other one, but not completely removes the correlation. It makes it really clear to me that how this approach works and what are the pros and cons.
Well, I myself has never tried this approach of minimizing the correlation between N*S02 and sigma2, but I read a lot about it in the literature. With my limited knowledge about the method, I could not judge this approach, although I had my own doubts.
I truly appreciate your efforts in providing me a deeper insight into this approach.
Best regards,
Jatin
-----Original Message-----
From: ifeffit-bounces@millenia.cars.aps.anl.gov
[mailto:ifeffit-bounces@millenia.cars.aps.anl.gov] On Behalf Of
ifeffit-request@millenia.cars.aps.anl.gov
Sent: 22 March, 2015 18:00
To: ifeffit@millenia.cars.aps.anl.gov
Subject: Ifeffit Digest, Vol 145, Issue 40
Send Ifeffit mailing list submissions to
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To subscribe or unsubscribe via the World Wide Web, visit
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Today's Topics:
1. Re: Breaking down correlationships between parameters
    (Matt Newville)
---------------------------------------------------------------------
-
Message: 1
Date: Sun, 22 Mar 2015 11:52:30 -0500
From: Matt Newville 
To: XAFS Analysis using Ifeffit 
Subject: Re: [Ifeffit] Breaking down correlationships between
      parameters
Message-ID:

Content-Type: text/plain; charset="utf-8"
Hi Jatin,
...
On Sat, Mar 21, 2015 at 10:41 AM, Rana, Jatinkumar Kantilal < jatinkumar.rana@helmholtz-berlin.de> wrote:
Hi Matt,
Thanks a lot for your prompt reply. The method I am referring to is
not the multiple k-weight fits by constraining N*S02. My apologies
for not being clear enough. Let's do it again. I am actually
referring to an approach where we take an advantage of a different
k-dependence of various parameters to breakdown correlations between
them. For example, S02 and sigma2. S02 is k-independent and Sigma2 has k^2 dependence.
Yes, I am familiar with this approach, and I understand that this is what you are using.  What I am saying is that this does not work nearly as well as (sometimes) claimed, and is sort of cheating.  It ignores the measures of statistical significance.
In this case, to breakdown correlation between S02 and sigma2,
The correlation between N*S02 and sigma2 is inherent to the finite k-range of the EXAFS signal.  It cannot be "broken", though it might be reduced.
...
one can assume a series of S02 values and perform fits using a
single k-weight each time (say k-weight 1,2 and 3) and record
corresponding
sigma2 values.
Let us say for k-weight =1, a series of preset S02 values will result
in a
...
series of corresponding sigma2 values refined in fits, which can be
plotted as a straight line in sigma2 vs. S02 plot.
OK, one can fit sigma2 with a series of preset values on N*S02.  That's fine.  But it does NOT lead to an infinitely thin line of sigma2 vs.
N*S02.  Each sigma2 value on that line has a width, corresponding to its
uncertainty.   In fact, the line you produce nicely demonstrates and
measures the correlation of N*S02 and sigma2 as the slope of this line.
...
Similar straight lines can be obtained for fits using k-weight = 2
and then 3.
Now, these three lines may intersect at or near some point, which
will
...
determine the "true" value of parameters independent of k-weight.
The different lines (each with finite thickness) will give a *range
of
values* for N*S02 and sigma2, not a single value.
The biggest problem with this approach is that it ignores the relative goodness-of-fits (let's just assume that is 'chi-square' for the purpose of
this discussion) for the fits along these lines.   Some fits are better
than others, and this approach completely ignores that fact, and equally importantly ignores the fact that there is a range of values for chi-square
that are consistent with "good".     If you include these values, your
linear plot will become contours of chi-square as a function of N*S02 and
sigma2.   And, yes, by using different k-weights and k-ranges and so on you
can get overlapping contour plots which may reduce the correlation a small amount when looked at as an ensemble.  And you can find a best set of values for N*S02 and sigma2, but *each* of these will have an uncertainty.
So, you can use this approach to find a good value for N*S02, but it is not breaking the correlation.  You can do this by hand.  Or you can just do a
fit with datasets with different k-weights and k-ranges.   When you do this
as a fit, you will see that the correlation is still fairly large.
Also, just to be clear, this is absolutely not a "true" value.  It is a measured value.  Not at all the same thing.
One can then constrain S02 to a value obtained from the point of
...
intersection of three lines and vary sigma2 in a fit.
Well, one can certainly set N*S02 to some value and fit sigma2.  As I said earlier, this ignores the correlation of N*S02 and sigma2, but does not remove that correlation.
...
In this particular case, however, the advantage is, S02 does not
depend on changes inside sample and we have very good estimate of
its range (say 0.7
- 1.0).
Now suppose instead of S02 (which i now set to a reasonable value),
I am interested in determining N, but it is highly correlated with
sigma2. Each time when disorder in the sample increases, the sigma2
increases and due to its high correlation, N is also overestimated.
On the other hand, when the disorder in the sample decreases, the
sigma2 decreases and I can have a "true" estimation of N in the
sample. Can I still apply the above mentioned approach to break the correlationship between N and sigma2 and get a "true"
estimation of N, even if disorder is high in my samples ? or it is
simply not possible due to the fact that both N and sigma2 varies
with changes inside the sample.
N and S02 are always 100% correlated (mathematically, not merely by the finite k range).  So, to the extent that the approach works at all, you can use it for "N" or "S02".  Really, the approach is comparing N*S02 and sigma2, in one case you asserted a value of "N" and projected all changes to "S02" -- you can equally assert "S02" and project all changes to "N".
To be clear,  this is not going to find the "true" value of anything, because no analysis is ever going to find the "true" value -- it's going to find a measured value.
Finally, the correlation of N*S02 and sigma2 does not imply a bias in the values for N*S02.  N*S02 is NOT overestimated because it is highly correlated with sigma2.
Hope that helps,
--Matt
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Rana, Jatinkumar Kantilal

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