C.28.MR:4.5 - Calculate the consequence under the retained conditions

Let Y_g(u) be the queried output obtained with replacement g and input u. For a finite input population with probabilities p(u), its mean is

E[Y_g] = sum_u p(u) Y_g(u).

Use the corresponding integral for a continuous input law when it exists. For a contrast between g and h in the same population, evaluate both under that population’s law. A paired simulation can reuse each joint input u for both computations. Preserve the dependence of inputs within each computation.

A symbolic expression, an inequality or a bound can be sufficient. Numerical precision should serve the receiving choice or explanation. If an estimate is required, distinguish its computational or sampling error from uncertainty about the causal model and its parameters.