Because of integrating out all Gs in all of the priors, interdependency between samples of α ij,pq |B ij,pq = b or β ij,pq |B ij,pq = b is introduced, resulting in simultaneously obtaining multiple samples impractical.
blocked sampling, which obtains sentence-level samples simultaneously Johnson et al., 2007a) is attractive for the fast mixing speed and the easy application of standard dynamic programming algorithms.