Dimension Reduction in Importance Sampling: Balancing Concentration and Exploration Through Variable Selection

This study introduces a new dimension-reduction method in importance sampling for stochastic simulation, addressing the curse of dimensionality inherent in traditional approaches. Grounded in the parsimony principle, we introduce a new metric tailored to the importance-sampling framework for effective variable selection. To evaluate this metric, we devise a cross-validation procedure that accounts for the unique challenges present within the importance-sampling context. The proposed method strikes a critical balance between concentrating on key variables and exploring broader input areas, thereby reducing variance and enhancing the robustness of estimated outcomes. Whereas broadly applicable, we demonstrate its effectiveness in a nonparametric importance-sampling setting. Additionally, coupled with sensitivity analysis, we quantify the role and significance of each selected variable. Numerical experiments and a wind turbine case study showcase the superior performance of our approach, outperforming existing methods. History: Kwok-Leung Tsui served as the senior editor for this article. Funding: This work was partly supported by the U.S. National