Videos

This is a tutorial for QMCPy, a Python library for quasi-Monte Carlo calculations, given at MCQMC 2020.

Abstract: Quasi-Monte Carlo (QMC) integration is a method for computing multidimensional integrals. It avoids the curse of dimensionality of classical quadrature rules in the same sense that plain Monte Carlo (MC) sampling does. When some randomization is injected into QMC, it is then superior to plain MC in several ways. It has a variance that is o(1/n) asymptotically while not being more than a given multiple of the MC variance at finite n. For favorable integrands, a better convergence rate is seen at practical sample sizes. One could wonder why QMC has not displaced MC. First, there is some modestly increased complexity to use it. Second, while it rarely underperforms plain MC, some skill may be required in order to get dramatic improvements at practical sample sizes. It helps that there are now good software implementations.