Given the parameters {π 0 , π, φ, K} of the HMM, the joint distribution over hidden states s and observations y can be written (with s 0 = 0): As Johnson (2007) clearly explained, training the HMM with EM leads to poor results in PoS tagging.
we can easily treat the HMM in a fully Bayesian way (MacKay, 1997) by introducing priors on the parameters of the HMM.