This work develops variants of the multilevel Monte Carlo (MLMC) estimator [Giles,2008] for the estimation of unbiased expectation statistics. Standard MLMC estimators suffer from approximation error bias in the estimation of expectation statistics. The new MLMC estimators are applicable to sequences of model approximations that have a rate-dependent decreasing approximation error that can be extrapolated to the zero error limit. Output quantities of interest of this form often arise in uncertainty quantification problems utilizing the numerical approximation of PDEs and/or numerical quadrature. The resulting new MLMC estimators not only provide unbiased expectation estimates but also exhibit a computational cost savings when compared to the standard MLMC estimator for this class of problems.

中文翻译：

---

基于序列外推的无偏期望的多层蒙特卡罗估计

这项工作开发了多级蒙特卡洛（MLMC）估计器的变体[Giles，2008]，用于估计无偏期望统计量。在期望统计量的估计中，标准MLMC估计器存在近似误差偏差。新的MLMC估计器适用于模型逼近序列，这些序列具有与速率相关的递减逼近误差，可以将其推断到零误差极限。在利用PDE的数值逼近和/或数值正交的不确定性量化问题中，经常会出现这种形式的目标输出量。与针对此类问题的标准MLMC估计器相比，所得的新MLMC估计器不仅提供了无偏的期望估计值，而且还节省了计算成本。