Motivated by various computational applications, we investigate the problem of estimating nested expectations. Building upon recent work by the authors, we propose a novel Monte Carlo estimator for nested expectations, inspired by sparse grid quadrature, that does not require sampling from inner conditional distributions. Theoretical analysis establishes an upper bound on the mean squared error of our estimator under mild assumptions on the problem, demonstrating its efficiency for cases with low-dimensional outer variables. We illustrate the effectiveness of our estimator through its application to problems related to value of information analysis, with moderate dimensionality. Overall, our method presents a promising approach to efficiently estimate nested expectations in practical computational settings.

翻译：受多种计算应用的驱动，本文研究了嵌套期望的估计问题。基于作者近年来的工作，我们受稀疏网格求积法启发，提出了一种无需从内层条件分布中采样的新型蒙特卡洛估计器。理论分析表明，在问题的温和假设条件下，该估计器均方误差存在上界，证明其在低维外层变量情形下具有高效性。通过将所提方法应用于中等维度的信息价值分析问题，我们验证了其有效性。总体而言，该方法为实际计算场景中高效估计嵌套期望提供了一种具有前景的途径。