Gradient estimation for applied Monte Carlo analyses

For many practical applications of system analysis by Monte Carlo simulation, an important piece of information is the sensitivity of the outcome to input information. One matter of interest is the sensitivity of the outcome of the variables controlling it, that is the gradients with respect to the (usually implicit) performance function. Typically, analytical first (and higher) derivatives are not available and the usual numerical approach requires major computational effort. The present paper proposes estimation of gradients using a simplified (linear) response surface, which is a function of the random variables, and which is constructed after the Monte Carlo simulation has been performed. It uses all, or a subset of, the simulation run outcomes. No extra simulation runs are required. There are few restrictions on the form of the performance function and the gradients are estimated at small computational cost. The present paper is restricted to normal random variables.