We consider the Gaussian framework for reverberant audio source separation, where the sources are modeled in the time-frequency domain by their short-term power spectra and their spatial covariance matrices. We propose three alternative probabilistic priors over the spatial covariance matrices which are consistent with the theory of statistical room acoustics and we derive Expectation-Maximization (EM) algorithms for maximum a posteriori (MAP) estimation. We argue that these algorithms provide a statistically principled solution to the permutation problem and to the risk of overfitting resulting from conventional maximum likelihood (ML) estimation. We show experimentally that, in a semi-informed scenario where the source positions and certain room characteristics are known, the algorithms using respectively inverse-Wishart and Gaussian priors outperform their ML counterparts. This opens the way to rigorous statistical treatment of this family of models in other scenarios in the future.