Multilevel Monte Carlo Metamodeling for Variance Function Estimation

This work introduces a novel multilevel Monte Carlo (MLMC) metamodeling approach for variance function estimation. Although devising an efficient experimental design for simulation metamodeling can be elusive, the MLMC-based approach addresses this challenge by dynamically adjusting the number of design points and budget allocation at each level, thereby automatically creating an efficient design. Theoretical analyses show that, under mild conditions, the proposed MLMC metamodeling approach for variance function estimation can achieve superior computational efficiency compared to standard Monte Carlo metamodeling while achieving the desired level of accuracy. Additionally, this work establishes the asymptotic normality of the MLMC metamodeling estimator under certain sufficient conditions, providing valuable insights for uncertainty quantification. Finally, two MLMC metamodeling procedures are proposed for variance function estimation: one to achieve a target accuracy level and another to efficiently utilize a fixed computational budget. Numerical evaluations support the theoretical results and demonstrate the potential of the proposed approach in facilitating global sensitivity analysis.