The study of intelligent vehicles (IVs) is an area developing very fast and has the potential to transform road transportation and personal mobility in the years to come. In order to evaluate and minimize risks in the dynamic environment of IVs, it is necessary to have an accurate representation of the system and the uncertainty; the system describing IVs will never be a perfect representation of the true physical process and relying on its accuracy may lead to unreliable estimations and predictions and hence lead to wrong decisions. We will take into account this discrepancy of the mathematical representation and the physical system and utilize a fully Bayesian approach to develop a novel Bayesian learning methodology enabling efficient decision-making such avoiding collisions, as well as robust fault diagnosis. By first analyzing and understanding the uncertainty of an individual IV, the aim is to move to the collective behavior of IVs. This methodology will be validated on a physical test-bed at the University of Cyprus. The proposed project is highly interdisciplinary and combines methods from Engineering (expertise of the supervisor) and Statistics (extensive experience of the ER whose research background blends with parallel developments in Computer Science such as Machine Learning). This fellowship will contribute to the boost and advancement of the ER's career and ensure a two-way transfer of knowledge by (1) enriching the ER’s research skills through a career development plan and (2) the ER will transfer to the host her expertise. The potential impact of the proposed Bayesian uncertainty quantification of IVs can be high and important for the society as a whole, as we are making a step to the right direction to make IVs part of our everyday lives. The project has been designed around a coherent plan with experiments that will examine specific research directions but will also provide valuable insights and draw conclusions on Bayesian learning for IVs.