Thrombus formation is one of the main issues in the development of blood-contacting medical devices. This article focuses on the modeling of one aspect of thrombosis, the coagulation cascade, which is initiated by the contact activation at the device surface and forms thrombin. Models exist representing the coagulation cascade by a series of reactions, usually solved in quiescent plasma. However, large parameter uncertainty involved in the kinetic models can affect the predictive capabilities of this approach. In addition, the large number of reactions of the kinetic models prevents their use in the simulation of complex flow configurations encountered in medical devices. In the current work, both issues are addressed to improve the applicability and fidelity of kinetic models. A sensitivity analysis is performed by two different techniques to identify the most sensitive parameters of an existing detailed kinetic model of the coagulation cascade. The results are used to select the form of a novel reduced model of the coagulation cascade which relies on eight chemical reactors only. Then, once its parameters have been calibrated thanks to the Bayesian inference, this model shows good predictive capabilities for different initial conditions.