ABSTRACT
This chapter explores some techniques of variance reduction, with a particular focus on importance sampling. Reducing the variance (either by modifying the simulation procedure, or transforming the problem) may help to accelerate the convergence of the Monte-Carlo method. Decreasing the variance by a factor 10 is equivalent asymptotically to decreasing the number of simulations (and hence the computational time) by a factor of 10 to achieve a given accuracy. This technique of variance reduction is based on a modification of the sampling distributions, in order to sample outputs that one consider more relevant for the problem at hand. This distribution modification is simply a change of probability, which is commonly used in statistics and probability. In statistics for example, the theory of the estimation by likelihood maximization is based on the study of the density of a parametric model with respect to a reference probability measure.
