Open AccessBayes–Turchin approach to XAS analysis
Author(s) -
Rehr J. J.,
Kozdon J.,
Kas J.,
Krappe H. J.,
Rossner H. H.
Publication year - 2005
Publication title -
journal of synchrotron radiation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.172
H-Index - 99
ISSN - 1600-5775
DOI - 10.1107/s0909049504027876
Subject(s) - x ray absorption fine structure , a priori and a posteriori , xanes , linear subspace , x ray absorption spectroscopy , fourier transform , spectral line , absorption (acoustics) , set (abstract data type) , algorithm , mathematics , computer science , computational physics , absorption spectroscopy , physics , optics , mathematical analysis , spectroscopy , philosophy , geometry , epistemology , quantum mechanics , astronomy , programming language
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.