These experiments can be done with PCFGs randomly sampled from any distribution, but the fact that maximizing data likelihood as the objective can give better models than arbitrary random models ensures that evaluations are tractable and meaningful.
this model defines a Chomsky normal form (CNF) PCFG as a matrix G of binary rule probabilities which is first drawn from the Dirichlet prior with a concentration parameter β: trees for sentences 1..N are then generated by drawing from a PCFG: each tree τ is a set {τ , τ 1 , τ 2 , τ 11 , τ 12 , τ 21 , ...} of category node labels τ η where η ∈ {1, 2} * defines a path of left or right branches from the root to that node.