POLYNOMIAL CHAOS AS A CONTROL VARIATE METHOD

We introduce a control variate Monte Carlo method to estimate E[f(X)] based on a polynomial chaos expansion for f(X). We analyze the mean square error of the control variate estimator when the coefficients of the polynomial chaos approximation are obtained from Monte Carlo simulation. For a fixed computational cost, we determine the optimal allocation of cost between approximating the polynomial chaos coefficients and estimating the expectation of the function with the control variate estimator. Then, we examine the effects of setting the control to a polynomial chaos approximation of a reduced model, formed by freezing the insignificant inputs of the original model using global sensitivity analysis. We introduce two other polynomial chaos-based control variate methods for the calculation of Sobol' sensitivity indices, and compare our methods numerically against crude Monte Carlo and an approach that only uses polynomial chaos. Finally, we present some applications to option pricing, and compute the sensitivities of IEEE 14 busbar power system.

Automated summary

This paper introduces a control variate Monte Carlo method for estimating E[f(X)], analyzing its mean square error and cost allocation, as well as examining the impact of using a simplified model. Through applications in option pricing and sensitivity analysis of power systems, the effectiveness of the method is demonstrated.