The probability of selecting a subtree pair is its number of occurrences in the corpus divided by the number of pairs in the corpus with the same root nodes as it: P (< e s , e t >) = |<es,et>| <us,u t >:r(<us,u t >)=r(<es,e t >) |<us,ut>| The probability of a derivation in DOT is the product of the probabilities of the subtree pairs involved in building that derivation.
the probability of derivation <s Again, a translation can be generated by many different derivations, so the probability of a translation w s ←→w t is the sum of the probabilities of its derivations: Selection of the most probable translation via Monte Carlo sampling involves taking a random sample of derivations and outputting the most frequently occurring translation in the sample.