Monte Carlo integration is a rough and ready technique for calculating high-dimensional integrals and dealing with nonsmooth integrands [4, 5, 6, 8, 9, 10, 11, 12, 13]. Although quadrature methods can be extended to multiple dimensions, these deterministic techniques are almost invariably defeated by the curse of dimensionality. For example, if a quadrature method relies on
quadrature points in one dimension, then its product extension to
dimensions relies on
quadrature points. Even in one dimension, quadrature methods perform best for smooth functions. Both Romberg acceleration and Gaussian quadrature certainly exploit smoothness.