Variance Reduction Under Exponential and Scattering Angle Biasing: An Analytic Approach

An analytic approach to calculate variance reduction under analog and biased Monte Carlo simulation of deep-penetration problems is presented. Within the framework of this formulation, the variance reduction characteristics of exponential biasing and a recently proposed scheme that couples exponential biasing to scattering angle biasing are studied. The advantages and disadvantages of the coupled scheme over exponential biasing on deep-penetration problems with varying scattering probability and anisotropy are clearly illustrated.