In nested simulation literature, a common assumption is that the experimenter can choose the number of outer scenarios to sample. This paper considers the case when the experimenter is given a fixed set of outer scenarios from an external entity. We propose a nested simulation experiment design that pools inner replications from one scenario to estimate another scenario's conditional mean via the likelihood ratio method. Given the outer scenarios, we decide how many inner replications to run at each outer scenario as well as how to pool the inner replications by solving a bi-level optimization problem that minimizes the total simulation effort. We provide asymptotic analyses on the convergence rates of the performance measure estimators computed from the optimized experiment design. Under some assumptions, the optimized design achieves $\cO(\Gamma^{-1})$ mean squared error of the estimators given simulation budget $\Gamma$. Numerical experiments demonstrate that our design outperforms a state-of-the-art design that pools replications via regression.

翻译：在嵌套模拟文献中，一个常见假设是实验者可以选择采样的外部场景数量。本文考虑实验者从外部实体获得一组固定外部场景的情况。我们提出一种嵌套模拟实验设计，通过似然比方法将来自一个场景的内部重复样本汇集起来，用于估计另一个场景的条件均值。给定外部场景后，我们通过求解一个最小化总模拟工作量的双层优化问题，决定在每个外部场景运行多少内部重复样本，以及如何汇集这些内部重复样本。我们对基于优化实验设计计算的性能度量估计量的收敛速度进行了渐近分析。在某些假设下，给定模拟预算 $\Gamma$，优化设计使估计量的均方误差达到 $\cO(\Gamma^{-1})$。数值实验表明，我们的设计优于通过回归汇集重复样本的最先进设计。