Contrast enhanced myocardial perfusion magnetic resonance imaging (MRI) is a promising technique, providing insight into how reduced coronary flow affects the myocardial tissue. Stenosis in a coronary vessel leads to reduced myocardial blood flow, but collaterals may secure the blood supply of the myocardium, with altered tracer kinetics. Due to a low signal-to-noise ratio, quantitative analysis of the signal is typically difficult to achieve at the voxel level. Hence, analysis is often performed on measurements that are aggregated in predefined myocardial segments, that ignore the variability in blood flow in each segment. The approach presented in this paper uses local spatial information that enables one to perform a robust analysis at the voxel level. The spatial dependencies between local response curves are modelled via a hierarchical Bayesian model. In the proposed framework, all local systems are analyzed simultaneously along with their dependencies, producing a more robust context-driven estimation of local kinetics. Detailed validation on both simulated and patient data is provided.