Convex non-negative matrix factorization is a blind signal separation technique that has previously demonstrated to be well-suited for the task of human brain tumor diagnosis from magnetic resonance spectroscopy data. This is due to its ability to retrieve interpretable sources of mixed sign that highly correlate with tissue type prototypes. The current study provides a Bayesian formulation for such problem and derives a maximum a posteriori estimate based on a gradient descent algorithm specifically designed to deal with matrices with different sign restrictions. Its applicability to neuro-oncology diagnosis was experimentally assessed and the results were found to be comparable to those achieved by state of the art methods in tumor type discrimination and consistently better in source extraction.