Counterfactual

Would this patient have recovered without the drug they in fact took? The question is about a world that did not happen, to a specific individual whose actual outcome you already know. That is strictly harder than asking what happens on average under treatment, and it is the level at which most explanations people want actually sit.

The three-step recipe is abduction, action, prediction: infer the unobserved noise terms from what actually happened, apply the intervention, then recompute. The catch is that counterfactuals are not identified from experimental data alone — two models can agree on every intervention and disagree about individuals — so the answer depends on assumptions no trial can settle. Explanations built on them inherit that.

p(Y sub _x'  = y | X = x, Y = y') asks about Y under x' for units that were observed at x with outcome y'. Abduction updates the noise distribution p(U | x, y'), then the intervention is applied in the model with that updated U. Because the joint over potential outcomes is not identified by interventions, this needs the full structural model rather than the interventional distribution.