Covariate adjustment is a commonly used method for total causal effect
estimation. In recent years, graphical criteria have been developed to identify
all valid adjustment sets, that is, all covariate sets that can be used for
this purpose. Different valid adjustment sets typically provide total effect
estimates of varying accuracies. Restricting ourselves to causal linear models,
we introduce a graphical criterion to compare the asymptotic variances provided
by certain valid adjustment sets. We employ this result to develop two further
graphical tools. First, we introduce a simple variance reducing pruning
procedure for any given valid adjustment set. Second, we give a graphical
characterization of a valid adjustment set that provides the optimal asymptotic
variance among all valid adjustment sets. Our results depend only on the
graphical structure and not on the specific error variances or edge
coefficients of the underlying causal linear model. They can be applied to
directed acyclic graphs (DAGs), completed partially directed acyclic graphs
(CPDAGs) and maximally oriented partially directed acyclic graphs (maximal
PDAGs). We present simulations and a real data example to support our results
and show their practical applicability.

本研究提出了一种基于图形的标准来比较不同有效调整集合提供的渐近方差，同时介绍一种简单的减少方差的修剪程序和提供最优渐近方差的有效调整集合的图形特征，并展示这些结果的实际应用性。

因果线性模型中通过调整实现高效总效应估计的图形标准

Graphical Criteria for Efficient Total Effect Estimation via Adjustment  in Causal Linear Models

Covariate adjustment is a widely used approach to estimate total causal
effects from observational data. Several graphical criteria have been developed
in recent years to identify valid covariates for adjustment from graphical
causal models. These criteria can handle multiple causes, latent confounding,
or partial knowledge of the causal structure; however, their diversity is
confusing and some of them are only sufficient, but not necessary. In this
paper, we present a criterion that is necessary and sufficient for four
different classes of graphical causal models: directed acyclic graphs (DAGs),
maximum ancestral graphs (MAGs), completed partially directed acyclic graphs
(CPDAGs), and partial ancestral graphs (PAGs). Our criterion subsumes the
existing ones and in this way unifies adjustment set construction for a large
set of graph classes.

本文提出一个关于因果模型的条件，用于从图形化因果模型中识别出不同类型的建模方法并对总因果效应进行变量调整，此条件具有必要性和充分性。

完整的广义调整准则

A Complete Generalized Adjustment Criterion

This paper is concerned with graphical criteria that can be used to solve the
problem of identifying casual effects from nonexperimental data in a causal
Bayesian network structure, i.e., a directed acyclic graph that represents
causal relationships. We first review Pearl's work on this topic [Pearl, 1995],
in which several useful graphical criteria are presented. Then we present a
complete algorithm [Huang and Valtorta, 2006b] for the identifiability problem.
By exploiting the completeness of this algorithm, we prove that the three basic
do-calculus rules that Pearl presents are complete, in the sense that, if a
causal effect is identifiable, there exists a sequence of applications of the
rules of the do-calculus that transforms the causal effect formula into a
formula that only includes observational quantities.

本文研究非实验数据中确定因果关系的图形准则，提出了 Pearl 的工作和 Huang 和 Valtorta 的算法，并证明了 Pearl 提出的基本 do-calculus 规则是完整的。