Atherosclerotic coronary artery disease, which can result in coronary artery stenosis, acute coronary artery occlusion, and eventually myocardial infarction, is a major cause of morbidity and mortality worldwide. Non-invasive characterization of coronary blood flow is important to improve understanding, prevention, and treatment of this disease. Computational simulations can now produce clinically relevant hemodynamic quantities using only non-invasive measurements, combining detailed three dimensional fluid mechanics with physiological models in a multi-scale framework. These models, however, require specification of numerous input parameters and are typically tuned manually without accounting for uncertainty in the clinical data, hindering their application to large clinical studies. We propose an automatic, Bayesian, approach to parameter estimation based. on adaptive Markov chain Monte Carlo sampling that assimilates non-invasive quantities commonly acquired in routine clinical care, quantifies the uncertainty in the estimated parameters and computes the confidence in local predicted hemodynamic indicators. (C) 2016 Elsevier Ltd. All rights reserved.