Generally, Monte Carlo simulations are not part of the diverse set of regularization methods explored in the standard literature (Louis 1989; Hansen 1992 Hansen , 1998 Kress 1999; Engl et al. 2000) , although Monte Carlo methods have been used for estimating the regularization parameters of standard regularization functionals (Ramani et al. 2008) . The concept of a statistical distribution of parameter values should be confused neither with the real population distribution of coexisting species in the sample mixture nor the estimate of the latter in the form of a calculated sizeand-shape distribution. Nevertheless, one could ask to what extent one can rely on the statistical nature of the noise in the data, in combination with noise amplification, to produce a parsimonious two-dimensional histogram of (s, f r )species populations. As an example, we compare in Fig. 6 the standard analysis of our model data with the 10 9 100 grid and Tikhonov regularization (6a) with the histogram of all distributions from 50 Monte Carlo iterations (each based on an exact standard fit with the 10 9 100 grid; 6b). After 50 iterations the histogram clearly shows multimodal and spiky behavior suggesting the presence of multiple species, in contrast to the single broad peak representing the smoothest solution of all that fit the originally measured data. Thus, the 50 Monte Carlo iterations do not provide an effective means to correctly identify the information content of the data. If, on the other hand, we are independently knowledgeable about the monodisperse nature of the sample, we can use the Bayesian approach (Brown et al. 2007 ) to calculate the size-and-shape distribution that is closest to a single peak, and these results are shown, for comparison, in Fig. 6c .