tract: The availability of many real-world driving datasets is a key reason behind the recent progress of object detection algorithms in autonomous driving. However, there exist ambiguity or even failures in object labels due to error-prone annotation process or sensor observation noise. Current public object detection datasets only provide deterministic object labels without considering their inherent uncertainty, as does the common training process or evaluation metrics for object detectors. As a result, an in-depth evaluation among different object detection methods remains challenging, and the training process of object detectors is sub-optimal, especially in probabilistic object detection. In this work, we infer the uncertainty in bounding box labels from LiDAR point clouds based on a generative model, and define a new representation of the probabilistic bounding box through a spatial uncertainty distribution. Comprehensive experiments show that the proposed model reflects complex environmental noises in LiDAR perception and the label quality. Furthermore, we propose Jaccard IoU (JIoU) as a new evaluation metric that extends IoU by incorporating label uncertainty. We conduct an in-depth comparison among several LiDAR-based object detectors using the JIoU metric. Finally, we incorporate the proposed label uncertainty in a loss function to train a probabilistic object detector and to improve its detection accuracy. We verify our proposed methods on two public datasets (KITTI, Waymo), as well as on simulation data. Code is released at this https URL.