[Ifeffit] Logicused in Artemis to do the error minimization

[Pralay K. Santra]

Dear Bruce,

Thanks a lot. It will help me a lot. I will go through the details of
the references which you had mentioned.

With regards,

Pralay.

On Mon, Mar 8, 2010 at 7:41 PM, Bruce Ravel <bravel at bnl.gov> wrote:
> 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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-- 
Research Student
Prof D. D. Sarma's Group
(http://sscu.iisc.ernet.in/DDSarma)
Solid State and Structural Chemistry Unit
Indian Institute of Science
Bangalore 560 012 INDIA

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