#DAG #causation In [[Judea Pearl|Judea Pearl's]] causal framework, directed acyclic graphs (DAGs) are graphical representations used to model causal relationships between variables. A DAG consists of nodes (also known as vertices) and directed edges (also known as arrows) connecting the nodes. The arrows in a DAG indicate the causal dependencies or influences between variables. For the use of this word the the context of web-based [[Workflow]], please see this [[Workflow DAG]]. The key characteristics of directed acyclic graphs in Pearl's framework are: 1. [[Directed edge|Directed Edges]]: The edges in a DAG are directed, meaning they have a specific direction or orientation. The direction of an edge represents the causal relationship between two variables. For example, if variable A influences variable B, there will be a directed edge from A to B. 2. Acyclic Nature: DAGs are acyclic, which means they do not contain any cycles or loops. This property ensures that there are no circular dependencies among variables. The absence of cycles is crucial for causal inference, as it allows for the identification of cause-effect relationships and prevents causal feedback loops. 3. Nodes and Variables: The nodes in a DAG represent variables or factors of interest in a system. Each variable is associated with a node, and the relationships between variables are captured by the directed edges between the nodes. Variables can be observed variables, representing measurable quantities, or latent variables, representing unobserved or hidden factors. 4. Causal Interpretation: The structure of a DAG provides a causal interpretation of the relationships between variables. The presence of a directed edge from one variable to another implies a causal influence or direct effect of the first variable on the second. The absence of an edge indicates the absence of a direct causal relationship. DAGs are a powerful tool in causal inference as they allow for the visualization, representation, and analysis of causal relationships in complex systems. They provide a formal graphical language for modeling and reasoning about causality, enabling researchers to make inferences about the effects of interventions or estimate causal effects from observational data. By analyzing the structure of a DAG, researchers can identify causal relationships, assess the presence of confounding factors, determine which variables should be controlled for in an analysis, and guide the formulation of causal hypotheses. Overall, directed acyclic graphs (DAGs) in Judea Pearl's causal framework are graphical representations used to model causal relationships between variables. They provide a visual and formal language for representing and reasoning about cause-effect relationships, enabling causal inference and analysis. # References ```dataview Table title as Title, authors as Authors where contains(subject, "DAG") or contains(subject, "Directed Acyclic Graph") sort title, authors, modified ```