Do-Calculus

The do-calculus is a set of three inference rules, developed by Judea Pearl, for determining when observational data can be used to answer interventional questions. It operates on causal graphs — directed acyclic graphs in which edges represent direct causal effects — and provides a purely graphical criterion for identifying causal effects from observational data.

The three rules govern when it is legitimate to substitute observational probabilities for interventional ones, when variables can be deleted from the graph, and when conditioning can be moved across the do-operator. The do-calculus is complete: if a causal effect is identifiable from observational data and a causal graph, the do-calculus can derive it. If it is not identifiable, no algorithm can derive it.

This completeness makes the do-calculus the formal backbone of modern causal inference. Its practical limitation is that it requires a correctly specified causal graph, and in systems where the causal structure is unknown or contested, the do-calculus cannot be applied without first solving the harder problem of causal discovery.