fitting with lots of variables
Hi, Just a quick question... Currently I'm fitting experimental spectra to feff results from two different atomic configurations to try and figure out which scenerio is a better fit and what the ultimate atom positions are.... In doing this I'm already fitting for different sigma^2 for each path (since I'm not dealing with a monoatomic system).... Now I think I would like to fit for each path's individual DelR (....previously I'd been fitting with eta*reff for each but I'm expecting the displacement about the core atom to be quite different than further away from it).... My problem is... I don't have enough independent points to accomodate all the variables given the paths included when fitting over a specific R range. Currently I figure I have at least 2 options: 1)(Assuming I'm already using the largest suitable k-range) -- Increase the r-range for the fit (i.e. if fitting the single scattering paths to 4 Ang requires 18 variables but I only have 15 independent points with r-range 1-4... perhaps increase the r-range 1-4.5 (18 ind. points in this case) or 1-5 (20 ind. points in this case) while still including the paths less than 4Ang in the fit. 2) Lump some of the paths' DelRs into expressions (i.e. having DelRs = eta1*reff, or eta2*reff, or eta3*reff etc for groupings of paths dependent upon distance from core atom). Any suggestions about these ideas, or any other ideas-- I greatly appreciate the input! Thanks a ton! -Kristine
On Wednesday 21 January 2004 01:28 pm, k-kupiecki@northwestern.edu wrote: Hi Kristine, It'll be interesting to hear what everyone else has to say, but I think I can offer a few tidbits of wisdom.
1)(Assuming I'm already using the largest suitable k-range) -- Increase the r-range for the fit (i.e. if fitting the single scattering paths to 4 Ang requires 18 variables but I only have 15 independent points with r-range 1-4... perhaps increase the r-range 1-4.5 (18 ind. points in this case) or 1-5 (20 ind. points in this case) while still including the paths less than 4Ang in the fit.
This will not necessarily solve the problem. If you increase the R range without intending to actually fit the additional peaks, you may be cheating in the sense that you are pumping up the value of the Nyquist criterion without actually using the additional information. Take an extreme example. Consider a very disordered material which has a single peak near 2 angstroms and no further peaks. You might, then, fit from 1-3 in R space. You could set Rmax to 5, thereby doubling the Nyquist criteria, but you almost certainly will not be changing the fit in any other way. That is, you are not using the additional range in R. Indeed, in my example, there is no additional information because there is only the one peak. The implicit assumption when you choose the R range is that you will then go ahead and actually try to fit those Fourier components. If your fitting model does not actually attempt to fit well between 4.5 and 5 Angstroms, then you are not really doing the right thing by fooling Artemis and Ifeffit into thinking that you are.
2) Lump some of the paths' DelRs into expressions (i.e. having DelRs = eta1*reff, or eta2*reff, or eta3*reff etc for groupings of paths dependent upon distance from core atom).
Now *this* is a good idea. That is, after all, what math expressions are all about. Most of the examples I give in the things I write discuss math expressions being used to build prior knowledge into a fit. Another use of restraints is to limit the freedom of a fit in the case when you are running out of infomation. In your case, you are making the assumption that groups of paths have path lengths (or, perhaps, changes in path length) which cannot be distinguished at the level of resolution offered by the data and by the fitting model. That happens all the time and is a perfectly good use of math expressions and constraints. One nice thing about doing these sorts of freedom-limiting constraints is that you can choose to expand them or lift them as you begin to understand more about your data. That is, you may impose this sort of constraint early on in the analysis, then realize later that your data does in fact allow lifting some or all of the constraint. A couple more things to think about. 1. You might consider simply asserting something about the fit. For example, you might choose to assert that s02 is 0.9 rather than float it. This may lead to some systematic error in the determination of sigma^2 values, but may help you find the freedom you need to determine delR values. 2. You can look for trends in data sets. For example, if you have data on the same material at many temperatures, you may notice that s02, averaged over all data sets, is (to make it up off the top of my head) 0.875 +/- 0.103. You may then assert that the s02 is 0.875 and continue on. There are lots of kinds of data sets in which you may look for trends. For instance, if you have a series of samples with different amounts of dopant, you might expect certain e0 or s02 (or even delR or sigma^2) values to be the same across all data sets. Looking for trends in data sets is a very powerful tool and is a good reason to measure data in series. For instance, if you have a feul cell material that is intended to be operated at some elevated temperature, you probably should measure it at that temperature *and* at several others so you can find the trends, HTH, B -- Bruce Ravel ----------------------------------- ravel@phys.washington.edu Code 6134, Building 3, Room 222 Naval Research Laboratory phone: (1) 202 767 5947 Washington DC 20375, USA fax: (1) 202 767 1697 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/
Kristine, I was just contemplating how I might answer your question from my experience when Bruce's e-mail came through, leaving me with nothing subsansive to say. Thanks, Bruce! He's right on the money in both areas. First, it's cheating to extend the R range when you're not trying to fit paths over that range. Second, if you need 18 parameters and you're only allowed 15, you're going to have to use math expressions, or fix some parameters at reasonable values taken from averages, commonly used assumptions (like S0^2 = 0.9), or from other similar systems. Mark Jensen -----Original Message----- From: ifeffit-bounces@millenia.cars.aps.anl.gov [mailto:ifeffit-bounces@millenia.cars.aps.anl.gov]On Behalf Of Bruce Ravel Sent: Wednesday, January 21, 2004 1:10 PM To: k-kupiecki@northwestern.edu; XAFS Analysis using Ifeffit Subject: Re: [Ifeffit] fitting with lots of variables On Wednesday 21 January 2004 01:28 pm, k-kupiecki@northwestern.edu wrote: Hi Kristine, It'll be interesting to hear what everyone else has to say, but I think I can offer a few tidbits of wisdom.
1)(Assuming I'm already using the largest suitable k-range) -- Increase the r-range for the fit (i.e. if fitting the single scattering paths to 4 Ang requires 18 variables but I only have 15 independent points with r-range 1-4... perhaps increase the r-range 1-4.5 (18 ind. points in this case) or 1-5 (20 ind. points in this case) while still including the paths less than 4Ang in the fit.
This will not necessarily solve the problem. If you increase the R range without intending to actually fit the additional peaks, you may be cheating in the sense that you are pumping up the value of the Nyquist criterion without actually using the additional information. Take an extreme example. Consider a very disordered material which has a single peak near 2 angstroms and no further peaks. You might, then, fit from 1-3 in R space. You could set Rmax to 5, thereby doubling the Nyquist criteria, but you almost certainly will not be changing the fit in any other way. That is, you are not using the additional range in R. Indeed, in my example, there is no additional information because there is only the one peak. The implicit assumption when you choose the R range is that you will then go ahead and actually try to fit those Fourier components. If your fitting model does not actually attempt to fit well between 4.5 and 5 Angstroms, then you are not really doing the right thing by fooling Artemis and Ifeffit into thinking that you are.
2) Lump some of the paths' DelRs into expressions (i.e. having DelRs = eta1*reff, or eta2*reff, or eta3*reff etc for groupings of paths dependent upon distance from core atom).
Now *this* is a good idea. That is, after all, what math expressions are all about. Most of the examples I give in the things I write discuss math expressions being used to build prior knowledge into a fit. Another use of restraints is to limit the freedom of a fit in the case when you are running out of infomation. In your case, you are making the assumption that groups of paths have path lengths (or, perhaps, changes in path length) which cannot be distinguished at the level of resolution offered by the data and by the fitting model. That happens all the time and is a perfectly good use of math expressions and constraints. One nice thing about doing these sorts of freedom-limiting constraints is that you can choose to expand them or lift them as you begin to understand more about your data. That is, you may impose this sort of constraint early on in the analysis, then realize later that your data does in fact allow lifting some or all of the constraint. A couple more things to think about. 1. You might consider simply asserting something about the fit. For example, you might choose to assert that s02 is 0.9 rather than float it. This may lead to some systematic error in the determination of sigma^2 values, but may help you find the freedom you need to determine delR values. 2. You can look for trends in data sets. For example, if you have data on the same material at many temperatures, you may notice that s02, averaged over all data sets, is (to make it up off the top of my head) 0.875 +/- 0.103. You may then assert that the s02 is 0.875 and continue on. There are lots of kinds of data sets in which you may look for trends. For instance, if you have a series of samples with different amounts of dopant, you might expect certain e0 or s02 (or even delR or sigma^2) values to be the same across all data sets. Looking for trends in data sets is a very powerful tool and is a good reason to measure data in series. For instance, if you have a feul cell material that is intended to be operated at some elevated temperature, you probably should measure it at that temperature *and* at several others so you can find the trends, HTH, B -- Bruce Ravel ----------------------------------- ravel@phys.washington.edu Code 6134, Building 3, Room 222 Naval Research Laboratory phone: (1) 202 767 5947 Washington DC 20375, USA fax: (1) 202 767 1697 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/ _______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
participants (3)
-
Bruce Ravel -
k-kupiecki＠northwestern.edu -
Mark Jensen