Figure 2.

Inside–outside algorithm. (A) Markov-like property for trees in branching processes: if a tree T₁ is split in two sub-trees T₂ and T₃, the probability of the original tree is the product of the probabilities of the two sub-trees. Also, the two sub-trees are independent conditional to the value of the node at the separation point. (B) The probabilities in the two sub-trees can be computed separately: the inside probability can be computed recursively in a bottom-up fashion, the outside probabilities can be computed recursively top-down.