The improvement range is from 2.59 (in Turkish-to-English) up to 2.99 (in English-to-Turkish) BLEU points in travel domain and from 0.16 (in English-to-Czech) up to 0.85 (in English-to-Arabic) BLEU points in news domain.
alignment inference in neither of these works is exactly Bayesian since the alignments are updated by running GIZA++ (Xu et al., 2008) or by local maximization (Nguyen et al., 2010).