If correlation doesn't imply causation, then what does?
statisticscausalityprobabilityinference
Abstraction: Judea Pearl's causal calculus inferring causation from observational data
Key points:
- Simpson's paradox: correlations can reverse entirely when a confounding variable is included (Civil Rights Act: Democrats had higher overall NO vote, yet higher YES rate in both North and South)
- Judea Pearl's causal models use directed acyclic graphs (DAGs) where each variable is a function of its parents plus independent noise
- The "do" operator represents experimental intervention, severing incoming edges to the intervened variable in the graph
- d-separation is a graph-theoretic criterion for conditional independence; colliders, forks, and traverses determine whether paths carry information
- Three rules of causal calculus allow deriving interventional probabilities from observational data without running controlled experiments; shown applicable to smoking-tar-cancer model
Connections: Judea Pearl · Michael Nielsen · Causal Inference · Simpsons Paradox · Directed Acyclic Graphs
Source: http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/