To calculate the posterior, we first use the definition of conditional probability to rewrite it as In a context-free grammar, given the syntactic category that dominates a string of words, the words' probability is independent from everything outside the category.
this is equivalent to 5.1.1 Posterior: the numerator's first term The first term in the numerator P (S * ⇒ w i 0 Xν) can be computed from a parse of w i 0 by summing forward probabilities of the form 5.1.2 Posterior: the denominator Similarly, the denominator P (S * ⇒ w j 0 λ) can be computed from a parse of w j 0 by summing forward probabilities of the form for all Y.