Understanding causal relations in dynamic systems is essential in epidemiology. While causal inference methods have been extensively studied, they often rely on fully specified causal graphs, which may not always be available in complex dynamic systems. Partially specified causal graphs, and in particular summary causal graphs (SCGs), provide a simplified representation of causal relations between time series when working spacio-temporal data, omitting temporal information and focusing on causal structures between clusters of of temporal variables. Unlike fully specified causal graphs, SCGs can contain cycles, which complicate their analysis and interpretation. In addition, their cluster-based nature introduces new challenges concerning the types of queries of interest: macro queries, which involve relationships between clusters represented as vertices in the graph, and micro queries, which pertain to relationships between variables that are not directly visible through the vertices of the graph. In this paper, we first clearly distinguish between macro conditional independencies and micro conditional independencies and between macro total effects and micro total effects. Then, we demonstrate the soundness and completeness of the d-separation to identify macro conditional independencies in SCGs. Furthermore, we establish that the do-calculus is sound and complete for identifying macro total effects in SCGs. Finally, we give a graphical characterization for the non-identifiability of macro total effects in SCGs.

翻译：理解动态系统中的因果关系在流行病学中至关重要。尽管因果推断方法已得到广泛研究，但其通常依赖于完全指定的因果图，而这在复杂的动态系统中可能并不总是可用的。部分指定的因果图，特别是摘要因果图，在处理时空数据时提供了时间序列间因果关系的简化表示，它省略了时间信息，专注于时间变量簇之间的因果结构。与完全指定的因果图不同，摘要因果图可以包含环，这使其分析和解释变得复杂。此外，其基于簇的特性引入了关于感兴趣查询类型的新挑战：宏观查询，涉及图中表示为顶点的簇之间的关系；以及微观查询，涉及图中顶点未直接可见的变量之间的关系。在本文中，我们首先清晰地区分了宏观条件独立性与微观条件独立性，以及宏观总效应与微观总效应。然后，我们证明了d-分离在识别摘要因果图中宏观条件独立性方面的可靠性和完备性。此外，我们确立了do-演算对于识别摘要因果图中宏观总效应的可靠性和完备性。最后，我们给出了摘要因果图中宏观总效应不可识别性的一个图形化表征。