RE: [Ifeffit] S02-Interpretation
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. Shelly
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
On Friday 16 April 2004 10:37 am, Matt Newville wrote:
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.
I also agree that doing multiple-k-weight fitting should be the bottom line. One of these threads started off with someone asking me about the mapping approach to S02/sigma^2, so I chose to answer that question directly. I don't think anyone would argue that it is easier use repeated kweight arguments in the feffit() command or to click multiple k-weight buttons in Artemis than it is to laboriously map out S02/sigma^2 for many k-weights. And, as Matt says, doing the MKW fit, one is sure to also find the minimum of chi-square. B -- Bruce Ravel ----------------------------------- ravel@phys.washington.edu Code 6134, Building 3, Room 405 Naval Research Laboratory phone: (1) 202 767 2268 Washington DC 20375, USA fax: (1) 202 767 4642 NRL Synchrotron Radiation Consortium (NRL-SRC) Beamlines X11a, X11b, X23b National Synchrotron Light Source Brookhaven National Laboratory, Upton, NY 11973 My homepage: http://feff.phys.washington.edu/~ravel EXAFS software: http://feff.phys.washington.edu/~ravel/software/exafs/
participants (3)
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Bruce Ravel -
Kelly, Shelly D. -
Matt Newville