Evaluation of EXAFS Data by a Bayesian Least Squares Estimation Method with General Constraints

Abstract

If ill‐conditioned inverse problems have to be solved and physical preinformation is available, the Bayesian estimation method is more appropriate than other regularization methods. The method is improved in that way, that constraints in the form of linear equations between the parameter and with finite confidence intervals, can be included. This enlarges the possibilities as compared with the deterministic constraints that has been used commonly up to now. Regarding the evaluation of EXAFS data, but also in other methods of experimental structure research, empirical rules of crystal chemistry as well as other measuring data may be utilized as preinformation in the regularization procedure.