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Machine-learning based classification techniques have been shown to be effective at detecting objects in complex scenes. However, the final results are often obtained from the alarms produced by the classifiers through a post-processing which typically relies on ad hoc heuristics. Spatially close alarms are assumed to be triggered by the same target and grouped together. Here we replace those heuristics by a principled Bayesian approach, which uses knowledge about both the classifier response model and the scene geometry to combine multiple classification answers. We demonstrate its effectiveness for multi-view pedestrian detection. We estimate the marginal probabilities of presence of people at any location in a scene, given the responses of classifiers evaluated in each view. Our approach naturally takes into account both the occlusions and the very low metric accuracy of the classifiers due to their invariance to translation and scale. Results show our method produces one order of magnitude fewer false positives than a method that is representative of typical state-of-the-art approaches. Moreover, the framework we propose is generic and could be applied to any detection-by-classification task.