Editing Importance sampling (section)

==== Translation ====

Another simple and effective biasing technique employs translation of the density function (and hence random variable) to place much of its probability mass in the rare event region. Translation does not suffer from a dimensionality effect and has been successfully used in several applications relating to simulation of [[digital communication]] systems. It often provides better simulation gains than scaling. In biasing by translation, the simulation density is given by

:<math> f_*(x)= f(x-c), \quad c>0 \,</math>

where <math>c\,</math> is the amount of shift and is to be chosen to minimize the variance of the importance sampling estimator.