Modeling dependence in simulation input: The case for copulas

We discuss copulas for incorporating dependence in the input distributions to a simulation model. We start by motivating the need for incorporating dependence in the primitive inputs to a simulation. Copulas are then introduced as a convenient and flexible model to incorporate dependence. We rigorously define copulas, introduce some of their basic properties, illustrate popular copula families, and discuss methods for copula estimation. Since this is an introductory tutorial, we have attempted to keep all exposition at a basic mathematical level without omitting important technical details. The oral presentation of this tutorial will include additional discussion on random variate generation, copula inference, and tail dependence.