The prior for all θ, p(θ), is the product of all Dirichlet distributions over all non-terminals A ∈ N : Since the Dirichlet distribution is conjugate to the Multinomial distribution, which we use to model the likelihood of trees, the conditional posterior of θ A can be updated as follows: which is still a Dirichlet distribution with updated parameter f r (t) + α r for each rule r ∈ R. Gibbs sampler The parameters of the PCFG model can be learned from an annotated corpus by simply counting rules.
parsing cannot be done directly with standard CKY as with standard PCFGs, so we use the Gibbs sampling algorithm presented in Johnson et al.