Preliminary work found that mixing with token-level Gibbs sampling is even slower in this model due to the tight constraints imposed by the switching variables-it is technically ergodic but exploring the state space requires many low probability moves.
the experiments described in this paper use sentence-level sampling instead of token-level sampling, first computing forward probabilities for the sequence and then doing sampling in a backwards pass; resampling the parameters for the probability distributions only requires computing the counts from the sampled sequence and combining with the hyperparameters.