Preprint SMU-HEP-10-13 Comparison of Algorithms for Monte Carlo Integration of a Multi-dimensional Gaussian Function

Monte Carlo integration of multi-dimensional Gaussian functions is widely applicable in the statistical analysis of functions of many variables, and such analysis is encountered in many fields of science. In this write-up, we compare two Monte Carlo integration algorithms from the Cuba library, Vegas, and Suave, in terms of convergence time and accuracy of evaluation of a multi-dimensional Gaussian integrand. This comparison is important for the analysis of parton distribution functions based on Monte Carlo sampling. In general, we find that Vegas is better suited for this kind of integration. We also conclude that Vegas has faster convergence when used with Mersenne Twister psuedo-random numbers and that Vegas is more accurate when used with Sobol quasi-random numbers.