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 ensembles of 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，能够降低涉及高计算成本科学模型积分估计的计算代价。我们提出了一种控制变量法的扩展——多层控制泛函（MLCF），该方法采用基于Stein方法的非参数控制变量与低成本多保真度模型集成，以获得更优性能。MLCF具有广泛的适用性。研究表明，当被积函数与密度函数光滑且维度并非极高时，MLCF具备快速收敛率。我们通过理论分析与数值实验（包括生态模型的贝叶斯推断算例）验证了所提方法的有效性。