- A directed cyclic graph (DAG) is a way of describing qualitative causal relationships among variables
- It is in the form of arrows pointing from one symbol/variable describing the direction of influence. Ex: A -> B means A directly influences B

Syracuse University

University of Michigan - Ann Arbor

Correlation is a relationship, yet causality indicates one event is the result of the occurence of another event.

Correlation is not equal to causality

To demonstrate the statement "correlations is not equal to causation", we may refer to the "Spurious Correlation" Website.

An interesting project: spurious correlations

During the pandemic (COVID-19), people followed the "stay at home" rule to keep safe. One interesting fact is: in many countries, the birth rate is even higher during this period. Do you think COVID-19 caused a high birth rate? Or are they simply correlated?

Does COVID-19 Cause High Birth Rate?

DAG is a type of causal graph. It indicates the direction of causation, and the directions are denoted with arrows.

DAG: Direct Acyclic Graph

Spurious Association

Conditional independencies come in two forms. 
1) They are statements of which variables should be associated with one another (or not) in the data. 
2) They are statements of which variables become dis-associated when we condition on some other set of variables.

The implication that some variable Y is not associated with some variable X, after conditioning on some other variable Z is written: Y ⊥⊥ X|Z.
D ⊥/⊥ A means D “is not independent of” A

If we now look at the data and find that any pair of variables are not associated, then something is wrong with the DAG

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