2 While Bayesian model selection is in principle straight-forward, it turns out to require the ratio of two integrals (for the "evidence" or marginal likelihood) that are often intractable to compute.
given a training corpus D of unsegmented sentences and model families G 1 and G 2 (here the "function word" adaptor grammars with left-peripheral and right-peripheral attachment respectively), the Bayes factor K is the ratio of the marginal likelihoods of the data: where the marginal likelihood or "evidence" for a model G is obtained by integrating over all of the hidden or latent structure and parameters θ: Here the variable θ ranges over the space ∆ of all possible parses for the utterances in D and all possible configurations of the Pitman-Yor processes and their parameters that constitute the "state" of the Adaptor Grammar G. While the probability of any specific Adaptor Grammar configuration θ is not too hard to calculate (the MCMC sampler for Adaptor Grammars can print this after each sweep through D), the integral in (31) is in general intractable.