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What is Pearl's backdoor criterion?

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Answer

  • To identify P(Y  ∣  do(T))P(Y\; \mid \;\mathrm{do}(T)) from observational data, find a set of variables Z such that: (1) Z blocks all backdoor paths from T to Y (paths starting with an arrow into T), (2) Z contains no descendant of T.
  • Then P(Y  ∣  do(T))  =  ΣzP(Y\; \mid \;\mathrm{do}(T))\; = \;{\Sigma}_{z} P(Y  ∣  T,  Z=z)P(Y\; \mid \;T, \;Z = z) P(Z=z).
  • Effectively: condition on all confounders, don't condition on mediators or colliders.
  • Foundation of causal DAG-based analysis.
Check yourself — multiple choice
  • Random
  • Find Z that blocks all backdoor paths from T→Y and contains no descendant of T → identifies do(T) via observational conditioning
  • Same as regression
  • Not real

Backdoor: block backdoor paths, avoid descendants of T → identifies causal effect.

#causal-inference

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