The use of prior information for extracting the post-edge background

Abstract

Abstract A new method for extracting the post-edge background μ 0 is proposed, the method of Bayesian smoothing. A further evolution of the smoothing spline method is considered as well. Both techniques are capable of taking into account the prior information: about the absorption edge shape, about positions, forms, and strengths of the peculiarities on the μ 0 due to multi-electron excitations. Besides, since the Bayesian approach works in terms of the posterior probability density functions, it is a natural way to determine the errors of the μ 0 construction, which has always been hardly resolvable for any other method. Even with use of the prior information, which narrows the posterior probabilities, the errors of μ 0 are shown to be essentially larger than the experimental noise. Thus, the traditional use of the latter in the definition of χ 2 residual function gives too high a χ 2 and, therefore, too optimistic errors of the fitting parameters.