Variance-reduced estimation of Third-order statistics using control variates with splitting

This work proposes an approach to improve the estimation accuracy and precision of the first three statistical moments of the response of uncertain systems by leveraging one or more low-fidelity models via Control Variates. The two main contributions are: (1) the derivation of explicit expressions for estimating the mean, variance, and third central moment; and (2) the incorporation of a Splitting technique that enables unbiased estimation of all sought moments. Compared to standard Monte Carlo simulation, the proposed method achieves the same precision with significantly fewer high-fidelity model evaluations, thus reducing the computational cost. The application of the proposed approach is also illustrated when dealing with high-dimensional problems.