In this paper, we propose a decision-making framework for autonomous driving at road intersections that determines appropriate maneuvers for an autonomous vehicle to navigate an intersection safely and efficiently (regarding making progress), even in the face of violation vehicles-one of the most challenging tasks in the domain of autonomous vehicles. The proposed framework uses a digital map to predict future paths of observed vehicles and then uses the predicted future paths to identify potential threats (vehicles) and collision areas, regardless of whether observed vehicles are obeying traffic rules at the intersection. Next, under an independent and distributed reasoning structure, it systematically, reliably, and robustly assesses the potential threats, even under incomplete and uncertain noise data, by way of a threat measure, Bayesian networks, and time window filtering. It then uses this information to determine appropriate maneuvers for the autonomous vehicle to navigate the intersection safely and efficiently. We have tested and evaluated the proposed framework through in-vehicle testing on a closed urban test road under traffic conditions inclusive of nonviolation and violation vehicles. In-vehicle testing results show the performance of the proposed framework to be sufficiently reliable for autonomous driving at intersections regarding reliability, robustness, safety, and efficiency.