Hierarchical Pitman-Yor processes (or their special case, hierarchical Dirichlet processes) have previously been used in NLP, for example, in the context of syntactic parsing (Liang et al., 2007;Johnson et al., 2007).
in all these cases the effective size of the state space (i.e., the number of sub-symbols in the infinite PCFG (Liang et al., 2007), or the number of adapted productions in the adaptor grammar (Johnson et al., 2007)) was not very large.