In our case, we sample one hidden specification tree t i while holding all other trees t −i fixed: where However directly solving the subproblem (1) in our case is still hard, we therefore use a Metropolis-Hastings sampler that is similarly applied in traditional sentence parsing problems.
the Hastings sampler approximates (1) by first drawing a new t i from a tractable proposal distribution Q instead of P (t i |w, t −i ).