Low-rank matrix approximation methods provide one of the simplest and most effective approaches to collaborative filtering. Such models are usually fitted to data by finding a MAP estimate of the model parameters, a procedure that can be efficiently performed even on very large datasets. However, unless the regularization parameters are tuned carefully, this approach is prone to overfitting because it finds a single point estimate of the parameters. In this paper we present a fully Bayesian treatment of the Probabilistic Matrix Factorization (PMF) model in which model capacity is controlled automatically by integrating over all model parameters and hyperparameters. We show that Bayesian PMF models can be efficiently trained using Markov chain Monte Carlo methods by applying them to the Netflix dataset, which consists of over 100 million user/movie ratings. The resulting models achieve significantly higher prediction accuracy than PMF models trained using MAP estimation.