In the estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the goal is to estimate the causal effect, it is not necessary to fix a single causal structure or probability distributions. In this paper, we first show from a Bayesian perspective that it is Bayes optimal to weight (average) the causal effects estimated under each model rather than estimating the causal effect under a fixed single model. This idea is also known as Bayesian model averaging. Although the Bayesian model averaging is optimal, as the number of candidate models increases, the weighting calculations become computationally hard. We develop an approximation to the Bayes optimal estimator by using Gaussian scale mixture distributions.

翻译：在估计线性结构因果模型(SCM)的因果关系时,通常的做法是首先确定因果结构,估计概率分布,然后计算因果关系。然而,如果目标是估计因果影响,就没有必要确定单一因果结构或概率分布。在本文件中,我们首先从巴伊西亚的角度显示,根据每个模型估计的因果影响优于(平均)重量,而不是根据一个固定的单一模型估计的因果影响。这个概念也称为Bayesian平均模型。虽然随着候选模型的增加,Bayesian平均模型是最佳的,但加权计算变得难以计算。我们通过使用高斯比例的混合物分布,对Bayes的最佳估计值进行了近似。