On biasing Gaussian noise in importance sampling: optimization and implementation

New results are presented on the optimization of the mean translation (MT) and variance scaling (VS) biasing schemes for nonlinear systems with Gaussian noise inputs. It is also demonstrated how to implement these schemes using conditional importance sampling (IS). The authors show how conditional IS can be used to implement MT biasing when the system has both Gaussian and non-Gaussian inputs and extend the asymptotic analysis of J.S. Sadowsky and J.A. Bucklew (1990) to obtain new results on the optimization and interaction of MT and VS biasing. They give a precise mathematical definition of what is required for a system to be moderately nonlinear, and they demonstrate that while MT is most efficient, VS in combination with optimized MT can add a degree of robustness with respect to severe nonlinearlity