标题： 方差减少均值比率估计器的控制变量 显示英文标题

标题： Control variates for variance-reduced ratio of means estimators

摘要： 控制变量方法是一种经典的方差减少技术，用于蒙特卡罗估计器，它利用相关的辅助变量而不引入偏差。在许多应用中，感兴趣的量可以表示为期望值的比率。我们提出了一种针对此类比率的方差减少估计器，该估计器将控制变量应用于分子和分母。控制变量系数是联合优化的，以最小化结果估计器的方差。这种方法理论上保证了方差减少，并自然扩展到近似控制变量。模拟研究显示了显著的方差减少，特别是在变量与控制变量之间的相关性较强时。该方法的实际价值通过一个多保真度飞机设计的应用案例进行了说明。 显示英文摘要

摘要： The control variates method is a classical variance reduction technique for Monte Carlo estimators that exploits correlated auxiliary variables without introducing bias. In many applications, the quantity of interest can be expressed as a ratio of expectations. We propose a variance-reduced estimator for such ratios, which applies control variates to both the numerator and the denominator. The control variate coefficients are optimized jointly to minimize the variance of the resulting estimator. This approach theoretically guarantees variance reduction and naturally extends to approximate control variates. Simulation studies show significant variance reduction, particularly when correlations between variables and control variates are strong. The practical value of the method is illustrated with a multi-fidelity aircraft design use case.