Dirac mixture distributions for the approximation of mixed effects models⋆

Mixed effect modeling is widely used to study cell-to-cell and patient-to-patient variability. The population statistics of mixed effect models is usually approximated using Dirac mixture distributions obtained using Monte-Carlo, quasi Monte-Carlo, and sigma point methods. Here, we propose the use of a method based on the Cramér-von Mises Distance, which has been introduced in the context of filtering. We assess the accuracy of the different methods using several problems and provide the first scalability study for the Cramér-von Mises Distance method. Our results indicate that for a given number of points, the method based on the modified Cramér-von Mises Distance method tends to achieve a better approximation accuracy than Monte-Carlo and quasi Monte-Carlo methods. In contrast to sigma-point methods, the method based on the modified Cramér-von Mises Distance allows for a flexible number of points and a more accurate approximation for nonlinear problems.