In this paper, we assume that cause–effect relationships among variables can be represented by a Gaussian linear structural equation model and a corresponding directed acyclic graph. For a set of intermediate variables that satisfies the front-door criterion, we provide the variance formula of the estimated mean outcome under an external intervention in which a treatment variable is set to a specified constant value. The variance formula proposed in this paper is exact, in contrast to those in most previous studies on estimating total effects. In addition, based on the variance formula, we formulate the mean squared error between a future sample and the estimated mean outcome with the external intervention.

在本文中，我们假设变量之间的因果关系可以用高斯线性结构方程模型和相应的有向无环图表示。对于满足前门标准的一组中间变量，我们提供了在外部干预下将估计的平均结果的方差公式，其中将治疗变量设置为指定的恒定值。与大多数以前的估计总效应的研究相反，本文提出的方差公式是精确的。另外，基于方差公式，我们在外部干预下制定了未来样本与估计平均结果之间的均方误差。