Propagating errors in small-angle scattering data treatment

The problem of error propagation using indirect methods for small-angle scattering data treatment is considered. In these methods, the number of parameters to be determined is normally larger than the maximum number of independent parameters predicted by the Shannon sampling theorem and the solution has to be regularized. It is shown in model examples that evaluation of the error propagation via the covariance matrix can lead to significant overestimation of the propagated errors. The reason is that the procedure involves inversion of an ill-conditioned matrix. As an alternative, the Monte Carlo simulation procedure is recommended.