XAFS spectroscopy. II. Statistical evaluations in the fitting problems

Details XAFS spectroscopy. II. Statistical evaluations in the fitting problems XAFS spectroscopy. II. Statistical evaluations in the fitting problems

2000-03-28

arxiv.org/abs/physics/0003087v1

Physics

Data Analysis, Statistics and Probability

10 pages, 4 figures, for freeware XAFS analysis program, see http://www.crosswinds.net/~klmn/viper.html

Scientific paper

The problem of error analysis is addressed in stages beginning with the case of uncorrelated parameters and proceeding to the Bayesian problem that takes into account all possible correlations when a great deal of prior information about the accessible parametr space is available. The formulas for the standard deviations and deviations with arbitrary confidence levels are derived. Underestimation of the errors of XAFS-function extraction is shown to be a source of unjustified optimistic errors of fitting parameters. The applications of statistical chi^2- and F-tests to the fitting problems are also discussed.

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