Input Uncertainty Quantification for Quantiles

Input models that drive stochastic simulations are often estimated from real-world samples of data. This leads to uncertainty in the input models that propagates through to the simulation outputs. Input uncertainty typically refers to the variance of the output performance measure due to the estimated input models. Many methods exist for quantifying input uncertainty when the performance measure is the sample mean of the simulation outputs, however quantiles that are frequently used to evaluate simulation output risk cannot be incorporated into this framework. Here we adapt two input uncertainty quantification techniques for when the performance measure is a quantile of the simulation outputs rather than the sample mean. We implement the methods on two examples and show that both methods accurately estimate an analytical approximation of the true value of input uncertainty.