[Ifeffit] number of independent points

[Bruce Ravel]

On Monday, October 10, 2011 10:48:25 am Kropf, Arthur Jeremy wrote:
> Perhaps there is a more subtle analysis of the data range, but I doubt
> it, since Matt is on record as suggesting that people not place too much
> emphasis on the exact value of N-idp, if I recall correctly.  You can
> scale your chi-square, reduced chi-square, and errors using whatever
> value of N-idp you prefer.

The papers by Rossner and Krappe (for instance,
http://dx.doi.org/10.1103/PhysRevB.66.184303) use a Bayesian approach
to evaluate the actual information content in an EXAFS signal.
Unsurprisingly, the Bayesian analysis finds something we should
already know -- the EXAFS signal is not an ideally packed sum of sine
waves.  Consequently, the actual information content is rather less
than the Nyquist criterion.

That is the context of the suggestion not to place to much emphasis on
the Nyquist number.  (Since Jeremy invoked Matt, I should say that I
suspect that Matt would more or less agree with what I am saying
here.)   It gives us a number to work with in evaluating the statistics
in Ifeffit.  The interpretation of Ifeffit's statistical analysis
(which is a simple Gaussian analysis for a problem that is ill-posed
in the Guassian sense) has been a frequent topic of conversation on
this mailinglist over the years.  It is also a topic in this talk that
I sometimes give: https://github.com/bruceravel/XAS-
Education/downloads/atea.pdf

All that said, the question of the formula used and the value reported
in Artemis is a valid one.  I don't recall off the top of my head,
but I will look at the codes.

B


-- 

 Bruce Ravel  ------------------------------------ bravel at bnl.gov

 National Institute of Standards and Technology
 Synchrotron Methods Group at NSLS --- Beamlines U7A, X24A, X23A2
 Building 535A
 Upton NY, 11973

 My homepage:    http://xafs.org/BruceRavel
 EXAFS software:  http://cars9.uchicago.edu/ifeffit/Demeter