Since the posterior samples are produced as a byproduct of Gibbs sampling while maximum poste-rior decoding requires an additional time consuming step that does not have much impact on scores, we used the posterior samples to produce the results in Table 1.
to MCMC, Variational Bayesian inference attempts to find the function Q(y, θ, φ) that minimizes an upper bound of the negative log likelihood (Jordan et al., 1999): The upper bound in (3) is called the Variational Free Energy.