Control variates are variance reduction techniques for Monte Carlo estimators. They can reduce the cost of the estimation of integrals involving computationally expensive scientific models. We propose an extension of control variates, multilevel control functional (MLCF), which uses non-parametric Stein-based control variates and multifidelity models with lower cost to gain better performance. MLCF is widely applicable. We show that when the integrand and the density are smooth, and when the dimensionality is not very high, MLCF enjoys a fast convergence rate. We provide both theoretical analysis and empirical assessments on differential equation examples, including a Bayesian inference for ecological model example, to demonstrate the effectiveness of our proposed approach.

翻译：控制变量法是针对蒙特卡洛估计的方差缩减技术，能够降低涉及计算密集型科学模型的积分估计成本。我们提出控制变量法的扩展——多层次控制泛函（MLCF），该方法通过非参数Stein型控制变量和低成本多保真模型实现性能提升。MLCF具有广泛适用性。研究表明：当被积函数与密度函数光滑且维度较低时，MLCF具有快速收敛特性。我们通过理论分析和微分方程实例（包括生态模型贝叶斯推断案例）的实证评估，验证了所提方法的有效性。