Equivalence classes of DAGs (represented by CPDAGs) may be too large to provide useful causal information. Here, we address incorporating tiered background knowledge yielding restricted equivalence classes represented by 'tiered MPDAGs'. Tiered knowledge leads to considerable gains in informativeness and computational efficiency: We show that construction of tiered MPDAGs only requires application of Meek's 1st rule, and that tiered MPDAGs (unlike general MPDAGs) are chain graphs with chordal components. This entails simplifications e.g. of determining valid adjustment sets for causal effect estimation. Further, we characterise when one tiered ordering is more informative than another, providing insights into useful aspects of background knowledge.

翻译：有向无环图（DAG）的等价类（以CPDAG表示）可能过于庞大，无法提供有用的因果信息。本文探讨如何融合层级背景知识，从而得到以"层级MPDAG"表示的受限等价类。层级知识在信息量和计算效率方面带来显著提升：我们证明层级MPDAG的构建仅需应用Meek第一规则，且层级MPDAG（不同于一般MPDAG）是具有弦分量结构的链图。这简化了因果效应估计中有效调整集的确定等问题。此外，我们刻画了何种层级排序比另一种包含更多信息，为背景知识的有效利用提供了洞见。