[Ifeffit] Short questions

[Mamadou Diallo]

Bruce
I enjoyed reading your US$0.02. It is actually worth US$100.0

Mamadou

Bruce Ravel wrote:

>On Wednesday 13 September 2006 13:29, Juan Antonio Maciá Agulló wrote:
>  
>
>>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?
>>    
>>
>
>Hmmm... neat-o.  Some random fraction of the Nyquist criterion is now
>known as "Scott Calvin's rule".  Cool ;-)
>
>Scott mostly covered this in his answer.  I just wanted to add my
>US$0.02.
>
>The Fourier-based analysis we do in EXAFS takes many of its ideas from
>signal processing.  In the cannonical signal processing problem, we
>measure a time series -- for instance the signal coming from a radio
>station.  We can do a Fourier transform of that time series and get a
>frequency spectrum -- the notes in the music that the radio station is
>broadcasting.  If we wanted to do some kind of analysis on the signal
>we receive from the radio station, we can ask how much data could we
>hope to extract from the signal.  Well, that quantity has something to
>do with how long (in time) we measure the signal -- if we measure for
>10 minutes we will have more information than if we measure for 5
>minutes.  So the information content is somehow proportional to
>delta_T (the amount of time spent measuring the time sequence).  If we
>then choose to analyze only a narrow range of frequency -- say one
>hertz to either side of middle C -- then we will be examining less
>information than if we examine an entire octave of the signal.  So the
>information content is somehow proportional to delta_f (the width of
>the frequency band we examine).  This is the Nyquist criterion: the
>information content in an analysis of a time sequence is proportional
>to delta_T * delta_f.  It turns out the proportionality constant is
>2/pi.
>
>In EXAFS, chi(k) is analogous to the time sequence and chi(R) is
>analogous to the frequency spectrum.  So the information content of
>the EXAFS signal is, at most, 2 * delta_k * delta_R / pi.  That is the
>Nip number computed by Ifeffit based on the range of the Fourier
>transform and the range of the fit.  In EXAFS the data are not ideally
>packed -- that is, EXAFS is not a sum of pure sine waves -- and the
>data are often quite noisy.  So real data may not support Nip worth of
>variable parameters.  What you called the "Calvin rule" is just a
>crude rule of thumb stating that one should be uncomfortable when the
>number of parameters starts getting close to the Nip because your real
>data may not support the independent evaluation of that many
>parameters.
>
>  
>
>>And finally, how are errors calculated in Artemis for the parameters N
>>(coordination number), deltaE0, S02, deltaR and sigma^2?
>>    
>>
>
>Errors are NOT calculated in Artemis (or in Ifeffit for that matter)
>for the path parameters, N, deltaE0, S02, deltaR and sigma^2.  Errors
>are calculated for the guess parameters.  The path parameters are
>written in terms of the guess (and set and def) parameters, possibly
>by rather complicated math expressions.  If you want to know the
>uncertainties in the evaluations of the path parameters, you need to
>propagate the errors in the fitting parameters through those math
>expressions.  Sadly, the software does not do that for you at this
>time.
>
>If you are asking how the errors in the guess parameters are computed,
>well Ifeffit uses a Levenberg-Marquardt non-linear minimization.  This
>involves the evaluation of a covarience matrix.  The uncertainties are
>the diagonal elements -- with the caveat that they are scaled by the
>square root of reduced chi-square.  That rescaling is conceptually
>identical to asserting that the fit is good and that the reduced
>chi-square should have been equal to 1.  Any decent book on statistics
>for the physical sciences will explain the L-M method, including the
>covarience matrix, in excruciating detail.
>
>HTH,
>B
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