Figure 14.

Causal conditioning and marginalizing. (A) Variables outside the transition of interest are treated as fixed background conditions (indicated by the red pins). The transition probabilities $p\left(v_t\right|v_{t-1})$ are conditioned on the state of these background variables. (B) When evaluating the strength of a causal link within the transition, the remaining variables in $G_u$ outside the causal link are causally marginalized; that is, they are replaced by an average across all their possible states. With B marginalized, the state of A by itself does not determine and is not determined by the occurrence $\{\mathrm{XOR}=1\}$.