[Ifeffit] Logicused in Artemis to do the error minimization

[Frenkel, Anatoly]

Bruce,
 
Some time ago I was trying to find a reference (and failed) explaining the relationship between the error bar reported by the fitting algorithm of ifeffit and one standard deviation in the fitting parameter. From your reply below it appears that they are the same ("error bars reported by ifeffit are 1 sigma").
 
I have read in a few old xafs papers stating, without proof, that the error bars (also obtained by the same Levenberg-Marquardt algorithm) in the fits correspond to the 95% confidence intervals which means that they are much larger than 1 sigmal, more like 3 sigma. 
 
Can you comment more on your statement about 1 sigma, or give a reference?
Thank you,
Anatoly
 


________________________________

From: ifeffit-bounces at millenia.cars.aps.anl.gov on behalf of Ravel, Bruce
Sent: Mon 3/8/2010 9:11 AM
To: XAFS Analysis using Ifeffit
Subject: Re: [Ifeffit] Logicused in Artemis to do the error minimization



On Monday 08 March 2010 01:24:17 am Pralay K Santra wrote:
> Dear All,
>
> After the final fitting in Artemis, we get the (i) total error; (ii) the
> final value of the parameters;  (iii) the error in the parameters as well
>  as (iv) the dependencies among the parameters. What is kind of logic used
>  in Artemis to calculate these values? Is it Genetic optimization procedure
>  used in this process? Can anyone help me by giving some references.
>
> I was going through the old posts and found two posts. One is this one:
> http://cars9.uchicago.edu/ifeffit/FAQ/FeffitModeling and the other one
> mentioned in the same.
>
> I am sorry to ask for some help which is not directly related to the XAFS.

I am not really clear how a question about error analysis could be
considered as not directly related to XAFS.  To my mind, error
analysis is at the foundation of any scientific activity.

Ifeffit uses a Levenberg-Marquardt steepest descent algorithm to find
the parameters values which minimize chi-squared, which is computed in
the standard fashion (Bevington's Data Reduction and Error Analysis
for the Physical Sciences is my favorite text on the subject).

The uncertainties are the diagonal elements of the covarience matrix,
albeit scaled by the square root of reduced chi-square.  The reason
for this is that it is somewhere between extraordinarily difficult and
impossible to fully evaluate the measurement uncertainty in an XAFS
experiment.  As a result, chi-square is scaled incorectly.  By
rescaling the diagonal elements of the covarience matrix, we are
assuming that every fit is a good fit and that the only problem is the
evaluation of uncertainties.  Thus, if a fit is -- by some criterion --
good and is the one that you want to publish, the error bars reported
by Ifeffit are 1-sigma error bars.

The correlations are taken from the off-diagonal elements of the
covarience matrix.  Those need not be scaled and aren't.

The formulas for chi-square, reduced chi-square, and the R-factor are
given on pages 16 and following of this postscript file
http://cars.uchicago.edu/~newville/feffit/feffit.ps

My own take, for what it's worth, on all of this is explained on pages
6 to 15 of this presentation:

   http://xafs.org/Workshops/APS2009?action=AttachFile&do=view&target=Ravel_advanced_topics.pdf

B

PS: Phys. Rev. B 70, 104102 (2004) and J. Synchrotron Rad. (2005). 12,
70-74 are interesting papers about Bayesian approaches to EXAFS
analysis.  Ifeffit does not do Bayesian analysis.  But you seem
interested, so I thought I would point them out.



--

 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/~ravel/software/exafs/
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