[Ifeffit] statistical parameters

[Kelly, Shelly D.]

Hi Stephano,

> Not sure I fully follow, as I am not talking about background
> removal, but in any case, shouldn't the ratio between chi^2 and
> reduced-chi^2 be an integer number, whichever? 

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.

> 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.  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 matter
as long as you are consistent.  

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 phase,
hence the 2dkdr/pi part. If this length is -- then a data set like 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.

HTH
Shelly





Shelly Kelly                   Bldg 203 RM E113
Skelly at anl.gov              Argonne National Laboratory
630-252-7376                 9700 S Cass Ave
www.mesg.anl.gov         Argonne, IL 60439
 
 
 

> -----Original Message-----
> From: ifeffit-bounces at millenia.cars.aps.anl.gov [mailto:ifeffit-
> bounces at millenia.cars.aps.anl.gov] On Behalf Of Stefano Ciurli
> Sent: Wednesday, December 14, 2005 11:16 AM
> To: Ravel, Bruce D.; XAFS Analysis using Ifeffit
> Subject: Re: [Ifeffit] statistical parameters
> 
> Bruce,
> 
> >According to what you said above, Nvar = 7, so nu=24.83, which is
much
> >closer to 23.54.
> 
> of course. My mistake. But still...
> 
> >That still seems bigger than rounding errors, though.
> 
> that's what I am saying...
> 
> >Here is my understanding of Ifeffit, but I am sure Matt can
elaborate.
> >Background removal uses the integer part of dk*dr*2/pi+1 to determine
> >the number of knots.  Fitting uses dk*dr*2/pi as a real number to
> >determine Nidp.  In any case, that's what Artemis reports when you
ask
> >it how many independent points in a project.  My memory is that I
> >checked it against Ifeffit's report of Nidp.
> 
> 
> Stefano
> --
> ____________________________________________
> 
> Stefano Ciurli
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> Department of Agro-Environmental Science and Technology
> University of Bologna
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> Italy
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