Statistical evaluations in the fitting problems

The problem of error analysis is considered taking into account all possible pair correlations and prior information about the accessible parameter space. 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 χ2- and F-tests to the fitting problems are also discussed.