RÉSUMÉ
Modern analysis of X-ray absorption fine structure (XAFS) is usually based on a traditional least-squares fitting procedure. Here an alternative Bayes-Turchin method is discussed which has a number of advantages. In particular the method takes advantage of a priori estimates of the model parameters and their uncertainties and avoids the restriction on the size of the model parameter space or the necessity for Fourier filtering. Thus the method permits the analysis of the full X-ray absorption spectra (XAS), including both XAFS and X-ray absorption near-edge spectra (XANES). The approach leads to a set of linear equations for the model parameters, which are regularized using the 'Turchin condition'. Also, the method naturally partitions parameter space into relevant and irrelevant subspaces which are spanned by the experimental data or the a priori information, respectively. Finally we discuss how the method can be applied to the analysis of XANES spectra based on fits of experimental data to full multiple-scattering calculations. An illustrative application yields reasonable results even for very short data ranges.
Sujet(s)
Théorème de Bayes , Analyse spectrale/méthodes , Méthode des moindres carrés , Métalloprotéines/composition chimique , Rayons XRÉSUMÉ
We analyze EXAFS oscillations in k-space with the FEFF code to obtain main-shell distances Rv and mean-square displacement parameters sigma2i for all single and multiple scattering paths i in the shells v up to a maximum shell radius Rmax. To quantify the uncertainty in the determination of these model parameters we take into account experimental errors and uncertainties connected with background subtraction, with the approximate handling of the electronic many-body problem in FEFF, and with the truncation of the multiple scattering series. The impact of these uncertainties on the Rv and sigma2i is investigated in the framework of Bayesian methods. We introduce an a priori guess of these model parameters and consider two alternative strategies to control the weight of the a priori input relative to that of the experimental data. We can take a model parameter space of up to 250 dimensions. Optionally we can also fit the coordination numbers Nj (j < or = v) and the skewness of the distribution of the Rv besides the Rv and sigma2i. The method is applied to 10K Cu K-edge and 300K Au L3-edge data to obtain model parameters and their a posteriori error correlation matrices.
