Meaningful sensitivities: A new family of simulation sensitivity measures

Sensitivity analysis quantifies how a model output responds to variations in its inputs. However, the following sensitivity question has never been rigorously answered: How sensitive is the mean or variance of a stochastic simulation output to the mean or variance of a stochastic input distribution? This question does not have a simple answer because there is often more than one way of changing the mean or variance of an input distribution, which leads to correspondingly different impacts on the simulation outputs. In this article we propose a new family of output-property-with-respect-to-input-property sensitivity measures for stochastic simulation. We focus on four useful members of this general family: sensitivity of output mean or variance with respect to input-distribution mean or variance. Based on problem-specific characteristics of the simulation we identify appropriate point and error estimators for these sensitivities that require no additional simulation effort beyond the nominal experiment. Two representative examples are provided to illustrate the family, estimators and interpretation of results.