Assume that it is required to generate two samples of n independent identically distributed random variables, (X1,...,Xn) and (Y1,...,Yn), where X1 and Y1 have densities f and g, respectively. If these samples are used in a simulation, and f is close to g, it is sometimes desirable to have close simulation results. This can be achieved by insisting that both samples agree in most of their components, that is, Xi=Yi for as many i as possible under the given distributional constraints. Samples with this property are said to be optimally coupled. In this paper, various methods of coupling two samples, a sequence of samples and an infinite family of samples are proposed and studied.
