A Bayesian surrogate modeling technique is proposed that may be able to predict an optimal bypass graft configuration for patients suffering with stenosis in the internal carotid artery (ICA). At the outset, this statistical technique is considered as a means for identifying key geometric parameters influencing haemodynamics in the human carotid bifurcation. This methodology uses a design of experiments (DoE) technique to generate candidate geometries for flow analysis. A pulsatile one dimensional Navier-Stokes solver incorporating fluid-wall interactions for a Newtonian fluid which predicts pressure and flow in the carotid bifurcation (comprising a stenosed segment in the internal carotid artery) is used for the numerical simulations. Two metrics, pressure variation factor (PVF) and maximum pressure (p(*)(m)) are employed to directly compare the global and local effects, respectively, of variations in the geometry. The values of PVF and p(*)(m) are then used to construct two Bayesian surrogate models. These models are statistically analyzed to visualize how each geometric parameter influences PVF and p(*)(m). Percentage of stenosis is found to influence these pressure based metrics more than any other geometric parameter. Later, we identify bypass grafts with optimal geometric and material properties which have low values of PVF on five test cases with 70%, 75%, 80%, 85%, and 90% stenosis in the ICA, respectively.5%, 80%, 85%, and 90% stenosis in the ICA, respectively.