# [Ifeffit] Question about statistics

John J Rehr jjr at uw.edu
Fri Mar 6 15:27:19 CST 2015

```Dear Olga,

Thanks for your interest in the Bayesian analysis codes.  I'm glad to
hear that your are interested in developing the method. Although some
prototype Bayes-Turchin based codes were developed by Josh Kas as part
of his  thesis research, the project was never fully integrated into the
IFEFFIT
package and progress stalled for lack of funding.  But there has also been
a
parallel effort to develop a Bayes-Turchin code by Elizabeta Holub-Krappe
and her colleagues in Chiba, Japan. and I would suggest that you ask her
for a copy of their BT code and documentation.   I think this topic will
also be discussed at the XAFS16 conf in Karlsruhe in Aug 2015 - will you be
there ?

With very best regards,
John

cc E. Holub-Krappe

On Fri, Mar 6, 2015 at 12:39 PM, Olga Kashurnikova <okash at mail.ru> wrote:

> Hello, Dr Matt Newville,
>
> Thank you very much for the answer.
>
> There is a message with some corrections in the next thread – the numbers
> of my hand try to check am I right about chi_square and error calculation
> in IFEFFIT, were not right in the first time. I will try to attach the
> calculation files later, it is not clear for me how they will be shown here.
>
> I will write the main question and then about Bayesian analysis for thread
> splitting if you don’t mind. These things are interconnected that’s why I
> didn’t split them.
>
> The main question was about how IFEFFIT calculates chi_square and to what
> minimization function it adds restraints, in case of k_space. What is the
> normalization? I thought it should be
> (N_idp/N_data)sum[(dat-model)^2/eps^2], and in k space only the real part
> of data compared with imaginary part of model, but my hand calculation for
> check this gave the different result. It is necessary for the choice of
> optimal restraint (it is chi^2 without normalization that I need to
> compare) and for normalization of errors for them to be covariance matrix
> of this chi^2, as of Krappe and Rossner. Restraint will change errors, of
> course, because covariance matrix is (Q+A)^(-1) where A is regularizer in
> restraint and Q is what should be without restraint. If Q is not invertible
> (in case of some parametra don’t influence spectrum) it is critical, and
> optimal A can be found to strictly divide the ‘parametra space’ and verify
> models. That’s why I need to rescale them well, because for bayes it should
> be chi^2=sum[(dat-model)^2/eps^2]+A*sum(x-x0)**2  (A is connected with a
> priori ranges of parametra, it should be not one number, but algorithm of
> finding optimal diagonal A matrix is harder and I think not with
> IFEFFIT/Larch help). It is the same as your (paramA-A_0)/eps_A restraint, I
> understood what formula should be for a restraint, but don’t understand how
> to weight data and restraint part. It were Krappe and Rossner who mentioned
> Tikhonov regularization if I remember right, and it is very close, if I
> understood the paper about this regularization. That’s what I mean in
> ‘doesn’t fit’: 4 coordination spheres (Gd-O, Gd-Gd,Gd-Hf, next Gd-O for
> instance, and only first is in separate peak) may be in the N_idp range,
> but are so correlated that without constraints or other structure model the
> fit give bad results – some parametra will leave the acceptable range etc,
> and I’m not sure that without a Bayesian analysis I can define the better
> model of constraints, and the sphere splitting is even more difficult to
> define.
>
> So, the main question is ‘how IFEFFIT calculates this, what is the
> formula’, because FEFFIT manual doesn’t give the k-space case, and the
> check was wrong. I can append calculation files in a while if needed (I
> need to convert from a program to iff file), though I wrote formulae and
> they may be can be verified without numerical values.
>
> Chi_square in your method is close to what should be minimized and for
> what the covariance matrix should be found in Bayesian analysis, with the
> right normalization, that’s why I ask if I could use IFEFFIT to calculate
> this with renormalization of the results. If I put the right normalization
> to restraint, I need only rescale chi_square and errors and then calculate
> what I need. It is not that I think IFEFFIT use Bayesian statistics, I
> understand there are different approaches.
>
>
>
> Thankful for your assistance,
>
> Olga Kashurnikova, MEPhI, Moscow
>
>
>
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>
>
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