The synthetic data sets (of R1, R2 and NOE values) are created by randomly picking new values on a Gaussian distribution (with a width given by the experimental uncertainties) around the values predicted by the optimized value(s) of the fitted model-free parameter(s) (or possibly around the experimental values). Model-free parameters are then fit to these synthetic data sets, and the resulting width of the distribution for each fitted model-free parameter is a measure of the error in that parameter.
Note that the ModelFree program allows us to use one set of model-free parameters for generating the predicted relaxation parameters (around which the synthetic data are distributed), and a second, different set of model-free parameters (specified by the -s flag) for fitting to the synthetic data. This feature is used in evaluating the F-statistic for comparison of two different models.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992) "Numerical Recipies: the art of scientific computing". Cambridge University Press, p. 684 ff.
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