In this paper we propose a novel approach for the audio-based detection of events. The approach adopts the bag of words paradigm, and has two main advantages over other techniques present in the literature: the ability to automatically adapt (through a learning phase) to both short, impulsive sounds and long, sustained ones, and the ability to work in noisy environments where the sounds of interest are superimposed to background sounds possibly having similar characteristics. The proposed method has been experimentally validated on a large database of sounds, including several kinds of background noise, which are superimposed to the sounds to be recognized. The obtained performance has been compared with the results of another audio event detection algorithm from the literature, showing a significant improvement.