A system for determining cardiovascular information for a patient, the system comprising: at least one computer system configured to: receive non-invasively obtained patient-specific data regarding a geometry of at least the patient's vasculature; create an anatomic model representing at least a portion of the patient's vasculature based on the patient-specific data; create a computational model of a blood flow characteristic based on the anatomic model; identify one or more of an uncertain parameter, an uncertain clinical variable, and an uncertain geometry; initialize a probability model by constructing a coarse stochastic space for one or more of the identified uncertain parameter, uncertain clinical variable, and uncertain geometry; determine a blood flow characteristic, and pressure drop, within the patient's vasculature based on the anatomic model and the computational model of the blood flow characteristic of the patient's vasculature; identify at least one location in the anatomic model where the pressure drop is the highest; and calculate, based on the probability model and the determined blood flow characteristic, a sensitivity of the determined blood flow characteristic to one or more of the identified uncertain parameter, uncertain clinical variable, and uncertain geometry by simulating or estimating the blood flow characteristic for each point in a set of points in the stochastic space, and repeatedly refining the stochastic space and simulating or estimating the blood flow characteristic for each point in a set of points in the refined stochastic space until a termination criterion is met, locations where the pressure drop in the model is highest being chosen as candidate locations to determine said termination criterion; and the initializing of the probability model comprises initializing stochastic collocation points, each point corresponding to a unique combination of parameters, and said refining of the stochastic space comprises incrementing the collocation level. receive non-invasively obtained patient-specific data regarding a geometry of at least the patient's vasculature; create an anatomic model representing at least a portion of the patient's vasculature based on the patient-specific data; create a computational model of a blood flow characteristic based on the anatomic model; identify one or more of an uncertain parameter, an uncertain clinical variable, and an uncertain geometry; initialize a probability model by constructing a coarse stochastic space for one or more of the identified uncertain parameter, uncertain clinical variable, and uncertain geometry; determine a blood flow characteristic, and pressure drop, within the patient's vasculature based on the anatomic model and the computational model of the blood flow characteristic of the patient's vasculature; identify at least one location in the anatomic model where the pressure drop is the highest; and calculate, based on the probability model and the determined blood flow characteristic, a sensitivity of the determined blood flow characteristic to one or more of the identified uncertain parameter, uncertain clinical variable, and uncertain geometry by simulating or estimating the blood flow characteristic for each point in a set of points in the stochastic space, and repeatedly refining the stochastic space and simulating or estimating the blood flow characteristic for each point in a set of points in the refined stochastic space until a termination criterion is met, locations where the pressure drop in the model is highest being chosen as candidate locations to determine said termination criterion; and the initializing of the probability model comprises initializing stochastic collocation points, each point corresponding to a unique combination of parameters, and said refining of the stochastic space comprises incrementing the collocation level. calculate, based on the probability model and the determined blood flow characteristic, a sensitivity of the determined blood flow characteristic to one or more of the identified uncertain parameter, uncertain clinical variable, and uncertain geometry by simulating or estimating the blood flow characteristic for each point in a set of points in the stochastic space, and repeatedly refining the stochastic space and simulating or estimating the blood flow characteristic for each point in a set of points in the refined stochastic space until a termination criterion is met, locations where the pressure drop in the model is highest being chosen as candidate locations to determine said termination criterion; and the initializing of the probability model comprises initializing stochastic collocation points, each point corresponding to a unique combination of parameters, and said refining of the stochastic space comprises incrementing the collocation level.