11.7 Review

  • The do-notation extends the language of conditional probability to include intervention on some variables and observing other variables.

  • A causal network is a belief network where P(Xparents(X))=P(Xdo(parents(X))) for each variable X – intervening on the parents of a variable has the same effect as observing them.

  • D-separation characterizes which conditional independencies follow from the independencies of a directed graphical model (belief network). The do-calculus extends d-separation to include interventions.

  • The do-calculus can be used to show cases where the effect of interventions can be computed from observational data, including the backdoor and front-door criteria.

  • There are cases, such as in Simpson’s paradox, where the probabilistic inferences depend on the causal model and not just the data.

  • Counterfactual reasoning can be used to answer “what-if” queries.

  • Causal assumptions can be used to go beyond randomized clinical trials, if the assumptions are accepted.