Perfusion weighted MRI has proven very useful for deriving hemodynamic parameters such as CBF, CBV and MTT. These quantities are important diagnostically, e.g. in acute stroke, where they are used to delineate ischemic regions. Yet the standard method for estimating CBF based on singular value decomposition (SVD) has been demonstrated to underestimate (especially high) flow components and to be sensitive to delays in the arterial input function (AIF). Furthermore, the estimated residue functions often oscillate. This compromises their physiological interpretation/basis and makes estimation of related measures such as flow heterogeneity difficult. In this study, we estimate perfusion parameters based on a vascular model (VM) which represents heterogeneous capillary flow and explicitly leads to monotonically decreasing residue functions. We use a fully Bayesian approach to obtain posterior probability distributions for all parameters. In simulation studies, we show that the VM method has less bias in CBF estimates than the SVD based method for realistic SNRs. This also applies to cases where the AIF is delayed. We employ our method to estimate perfusion maps using data from (i) a healthy volunteer and (ii) from a stroke patient.