PROPAGATING ERRORS IN SMALL-ANGLE SCATTERING DATA TREATMENT

The problem of error propagation using indirect methods for small-angl e scattering data treatment is considered. In these methods, the numbe r of parameters to be determined is normally larger than the maximum n umber of independent parameters predicted by the Shannon sampling theo rem and the solution has to be regularized. It is shown in model examp les 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 rec ommended.