Myocardial perfusion can be quantified from dynamic contrast-enhanced MRI. This facilitates a non-invasive, automated, fast and user-independent evaluation of myocardial blood flow. However, due to the relatively low SNR, low temporal resolution and short scanning time the model fitting can yield unreliable parameter estimates. To counter-act this, simplified models and segmental averaging are used. In this work, Bayesian inference is employed. The inclusion of both spatial prior knowledge and prior knowledge of the kinetic parameters improves the reliability of the parameter estimation. This allows the generation of accurate high-resolution voxel-wise quantitative perfusion maps that clearly delineate areas of ischaemia.