Differential sampling for the Monte Carlo practitioner

One of the two methods for performing a perturbation calculation using Monte Carlo simulations is by differential sampling. The fundamental theory of differential sampling in Monte Carlo is well-presented in the literature but algorithms for implementation of the theory are not well-documented. The development of a differential sampling scheme and its implementation from the viewpoint of the Monte Carlo practitioner are presented here. Simplified examples of radiation transport and criticality of a multiplying system are used to illustrate the algorithms for implementation. Notes on applying the same schemes to more complex problems are also discussed.