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We present a novel approach to 3D object detection in scenes scanned by LiDAR sensors, based on a probabilistic representation of free, occupied, and hidden space that extends the concept of occupancy grids from robot mapping algorithms. This scene representation naturally handles LiDAR sampling issues, can be used to fuse multiple LiDAR data sets, and captures the inherent uncertainty of the data due to occlusions and clutter. Using this model, we formulate a hypothesis testing methodology to determine the probability that given 3D objects are present in the scene. By propagating uncertainty in the original sample points, we are able to measure confidence in the detection results in a principled way. We demonstrate the approach in examples of detecting objects that are partially occluded by scene clutter such as camouflage netting.