Bayes-Turchin approach to XAS analysis

Abstract

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. © 2005 International Union of Crystallography Printed in Great Britain - all rights reserved.