RE: [Ifeffit] statistical parameters
Hi Stephano
Since 2dkdr/pi is not always an integer number, the degrees of freedom which is the NIP (number of independent points) - number of variables is not always an integer number.
but I notice that in all papers this is reported as an integer number, which makes sense. DOes it mean I have to round it up to the closest integer? Plus, in the conversion from chi^2 to reduced-chi^2, does IFEFFIT consider it as an integer number or not?
[Kelly, Shelly D.] Well, In my opinion that depends on where you are publishing the data. If you are publishing the data in PRB then you should use the XX.X number. If you are publishing in Science Magazine then you should use the rounded number. If the answer depends on weather or not you round the number then I'd be suspicious. Often we round the number so that we don't have to explain why we have a non-integer numbers. You need ~ a factor of 2 for there to be a statistically significant difference in the reduced chi squared. So 33.5, 30, and 40 are all about the same number. Therefore I would round them all off to the nearest whole number that works. I like to show changes in the reduced chi square rather than the absolute value. Instead of showing a reduced-chi-square of 100 and 350, I show them as 1 and 3.5. Then you can say that 3.5 is much bigger than 1 so the model that gave 1 is the best. It is the relative change in the reduced chi square that matters. We get the absolute value wrong for a number of reasons. By showing the change you can side step all that explanation.
Plus, I have found a few documents in which Matt reports Nidp as 2dkdr/pi, some others in which he reports 2dkdr/pi+1. In SK's thesis, which is available on the net (thanks Shelly :-)) she says +2. I was simply wondering which is the right formula used in IFEFFIT, and if it is different from what reported in Stern, Phys. Rev. B, 1993, 48, 9825-9827, why it is so.
Most importantly, all of these expressions for the number of independent points are similar.
I know, but since I am reporting in a paper we are writing a table in which we show chi^2, reduced chi^2, Nidp and Npar (and therefore the degress of freedom) I was trying to be tidy and rigorous. But I am facing numbers which I cannot make much sense of.
[Kelly, Shelly D.] [Kelly, Shelly D.] That seems to be a problem. Are you processing the data with more than one k-weight in IFEFFIT? Try a test case were you use only one k-weight and see if you like the answers better. If you use more than one k-weight then the answers should be averages for all three data sets.
The most important part is that the number of independent points goes like 2dkdr/pi. When fitting EXAFS data you really need to have a lot more independent points than the number of fitted variables. In that case the +0, +1, or +2 doesn't really
as long as you are consistent.
of course, but see above.
The +1 and +2 come from the information at the beginning of the data set. I think of the raw chi(k) data as being chopped up into pieces with the length of each piece about dk ~ pi/dr. For every multiple of this length you get two data points representing an amplitude and
hence the 2dkdr/pi part. If this length is -- then a data set like
matter phase, this
.--.--.--.--.- Has 4.5 independent points, plus the one at the beginning hence +1 (count the "."). Now often Fourier transforms are done from r=0 to some other bigger r value. At the special value of r=0 you only need one variable, the amplitude, since the phase is known, hence 2dkdr/pi + 1. For EXAFS analysis we never start at r=0 so we get two parameters for each length, hence 2drdk/pi + 2.
OK. This is the sense of the paper by Stern, which now I understand better, thanks! Stefano -- ____________________________________________
Stefano Ciurli Professor of Chemistry Laboratory of Bioinorganic Chemistry Department of Agro-Environmental Science and Technology University of Bologna Viale Giuseppe Fanin, 40 I-40127 Bologna Italy Phone: +39-051-209-6204 Fax: +39-051-209-6203
"Fatti non foste a viver come bruti, ma per seguir virtute e canoscenza" Dante Alighieri - Inferno - Canto XXVI
"Ihr seid bestimmt, nicht Tieren gleich zu leben, Nein, Tugend zu erringen und Erkenntnis" "Ye were not form'd to live the life of brutes, But virtue to pursue and knowledge high" _______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
Hi Stefano, Check out this paper: H. J. Krappe and H. H. Rossner, Phys. Rev. B 61, 6595 (2000). The authors use a Bayesian analysis, and if I recall correctly, they determine that the amount of actual information present is considerably less than that given by the commonly used Nyquist criterion. That's because the Nyquist criterion assumes "ideally packed" information, as if EXAFS was a designed radio signal. Of course, the EXAFS gods had no particular reason to send us information in that form, so the information content is somewhat lower. To me, that makes the debate between +0, +1, and +2 somewhat moot...lacking a better method, I generally figure I should avoid having Nvar more than about 2/3 of Nidp, which is certainly satisfied in your case. Personally, I use the +0 formula when reporting the number of independent points, since it is the most conservative of the commonly used choices. --Scott Calvin Sarah Lawrence College
Hi everybody,
Hi Stefano,
Check out this paper:
H. J. Krappe and H. H. Rossner, Phys. Rev. B 61, 6595 (2000).
Just a detail: it's page 6596.
The authors use a Bayesian analysis, and if I recall correctly, they determine that the amount of actual information present is considerably less than that given by the commonly used Nyquist criterion. That's because the Nyquist criterion assumes "ideally packed" information, as if EXAFS was a designed radio signal. Of course, the EXAFS gods had no particular reason to send us information in that form, so the information content is somewhat lower. To me, that makes the debate between +0, +1, and +2 somewhat moot...lacking a better method, I generally figure I should avoid having Nvar more than about 2/3 of Nidp, which is certainly satisfied in your case. Personally, I use the +0 formula when reporting the number of independent points, since it is the most conservative of the commonly used choices.
Best regards - Michel
Hi Scott,
I use the +0 formula when reporting the number of independent points, since it is the most conservative of the commonly used choices.
will do the same, also because this is what I understand from Matt's message IFEFFIT does. Thanks! Stefano -- ____________________________________________ Stefano Ciurli Professor of Chemistry Laboratory of Bioinorganic Chemistry Department of Agro-Environmental Science and Technology University of Bologna Viale Giuseppe Fanin, 40 I-40127 Bologna Italy Phone: +39-051-209-6204 Fax: +39-051-209-6203 "Fatti non foste a viver come bruti, ma per seguir virtute e canoscenza" Dante Alighieri - Inferno - Canto XXVI "Ihr seid bestimmt, nicht Tieren gleich zu leben, Nein, Tugend zu erringen und Erkenntnis" "Ye were not form'd to live the life of brutes, But virtue to pursue and knowledge high"
Hi Shelly,
[Kelly, Shelly D.] Well, In my opinion that depends on where you are publishing the data. If you are publishing the data in PRB then you should use the XX.X number. If you are publishing in Science Magazine then you should use the rounded number.
clear as water :-)
If the answer depends on weather or not you round the number then I'd be suspicious.
this is not my case. I will use the XX.X number in the table. I will submit the paper to a biophysics type journal. I have now the arguments to have a dialogue with an hypothetical referee.
Often we round the number so that we don't have to explain why we have a non-integer numbers.
clear
You need ~ a factor of 2 for there to be a statistically significant difference in the reduced chi squared. So 33.5, 30, and 40 are all about the same number. Therefore I would round them all off to the nearest whole number that works. I like to show changes in the reduced chi square rather than the absolute value. Instead of showing a reduced-chi-square of 100 and 350, I show them as 1 and 3.5. Then you can say that 3.5 is much bigger than 1 so the model that gave 1 is the best. It is the relative change in the reduced chi square that matters.
got it
We get the absolute value wrong for a number of reasons. By showing the change you can side step all that explanation.
ok
I know, but since I am reporting in a paper we are writing a table in which we show chi^2, reduced chi^2, Nidp and Npar (and therefore the degress of freedom) I was trying to be tidy and rigorous. But I am facing numbers which I cannot make much sense of.
[Kelly, Shelly D.] That seems to be a problem. Are you processing the data with more than one k-weight in IFEFFIT?
no, we use only a k^3 weight I'll go read now Matt's mail... Thanks Stefano -- ____________________________________________ Stefano Ciurli Professor of Chemistry Laboratory of Bioinorganic Chemistry Department of Agro-Environmental Science and Technology University of Bologna Viale Giuseppe Fanin, 40 I-40127 Bologna Italy Phone: +39-051-209-6204 Fax: +39-051-209-6203 "Fatti non foste a viver come bruti, ma per seguir virtute e canoscenza" Dante Alighieri - Inferno - Canto XXVI "Ihr seid bestimmt, nicht Tieren gleich zu leben, Nein, Tugend zu erringen und Erkenntnis" "Ye were not form'd to live the life of brutes, But virtue to pursue and knowledge high"
participants (4)
-
Kelly, Shelly D. -
Michel Schlegel -
Scott Calvin -
Stefano Ciurli