Abstract

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.

摘要

敏感性分析量化了模型输出如何响应其输入的变化。然而，以下敏感性问题从未得到严格回答：随机模拟输出的均值或方差对随机输入分布的均值或方差有多敏感？这个问题没有简单的答案，因为通常有不止一种方法可以改变输入分布的均值或方差，这会导致对模拟输出的相应影响不同。在本文中，我们为随机模拟提出了一系列新的输出特性相对于输入特性的敏感性度量。我们关注这个一般家族的四个有用成员：输出均值或方差相对于输入分布均值或方差的敏感性。基于模拟的特定问题特征，我们为这些敏感性确定了适当的点和误差估计量，除了标称实验之外不需要额外的模拟工作。提供了两个具有代表性的例子来说明结果的族、估计量和解释。