Unsupervised learning of linguistic structure is a difficult problem. A common approach is to define a generative model and maximize the probability of the hidden structure given the observed data. Typically, this is done using maximum-likelihood estimation (MLE) of the model parameters. We show using part-of-speech tagging that a fully Bayesian approach can greatly improve performance. Rather than estimating a single set of parameters, the Bayesian approach integrates over all possible parameter values. .