[Ifeffit] Short questions

[Scott Calvin]

Hi JA,

Oh dear, I seem to have gotten a rule named after 
me that I didn't even know I'd put down in print. 
As I recall, I got it from an offhand comment by 
Bruce, and he may have gotten it from Rossner and Krappe... :)

Here's the deal in a nut-shell:

The Nip you give is the Nyquist criterion. Or 
it's the Nyquist criterion +1, or the Nyquist 
criterion +2. In any case, the Nyquist criterion 
was developed for a signal. If I want to give you 
information in a periodic signal, how much 
information can I give you using a certain 
bandwidth and time? That's what Nyquist tells you.

But there's no reason that Nature had to be so 
kind as to pack the maximum possible amount of 
information into an EXAFS signal. Some of the 
information may be redundant in some sense. So 
the true number of independent points might be somewhat less than Nip.

The 2/3 is purely made up, as far as I know. It's 
like saying the fit is pretty close to the data 
when the EXAFS R-factor is less than 0.02. That 
0.02 is arbitrary, but works as a rule of thumb.

I myself don't always pay attention to the 2/3 
that I have occasionally mentioned. I'm pretty 
sure I published stuff that's had more free parameters than that.

In sum, I think it's bad to think that there is 
some magic number of free parameters, below which 
you're OK, and above which you're not. The fewer 
free parameters you can get away with, the 
better. And you should always give the k-space 
and r-space ranges in your publications, along 
with the number of free parameters, so that 
people can draw their own conclusions. If I see a 
published fit with 15 independent points by the 
Nyquist criterion and 14 free parameters, I'm not 
going to discount it completely, but I will be 
somewhat more skeptical than if it had only 4 
free parameters, all else being equal.

Hope that helps.

--Scott Calvin
Sarah Lawrence College

At 02:29 PM 9/13/2006, Juan Antonio Maciá Agulló wrote:

>Hi Ifeffit people,
>
>I have a couple of short questions for you. I used the "Scott Calvin's
>rule" (number of variables < 2/3*Nip) to calculate the maximum number of
>allowed free parameters but I read that some people use the Nyquist
>theorem, which are the differences between them? and, which one is more
>correct?