Do operator

The do operator is used in causal inference to denote an intervention. Given random variables $X,Y$, we write $\Pr(Y=y\mid {\mathit {do}}(X=x))$ to mean the probability that $Y=y$ given we intervene and set $X$ to be $x$. In some texts, this is abbreviated to $\Pr(y\mid {\hat {x}})$ (this notation assumes that the random variables corresponding to the individual values are clear from context). The notation $\Pr _{x}(y)$ is also used.

In general $\Pr(Y=y\mid {\mathit {do}}(X=x))$ is not the same as conditioning on $X=x$, i.e. $\Pr(Y=y\mid X=x)$.

The do operator is used extensively in the do calculus.