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

A new method for extracting the post-edge background μ0 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 μ0 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 μ0 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 μ0 are shown to be essentially larger than the experimental noise. Thus, the traditional use of the latter in the definition of χ2 residual function gives too high a χ2 and, therefore, too optimistic errors of the fitting parameters.