Sensitivity Analysis for Simulations via Likelihood Ratios

Abstract

We present a simple method of estimating the sensitivity of quantities obtained from simulation with respect to a class of parameters. Here sensitivity means the derivative of an expectation with respect to a parameter. The class of parameters includes, for example, Poisson rates, discrete probabilities, and the mean and variance of a Normal distribution. The method is extremely well suited to regenerative simulation, and can be implemented on extant simulations with little effort, increase in running time, or memory requirements. It is based on some change-of-measure formulas derived from likelihood ratios. In addition to the theorems that underly the technique, we present some numerical examples.