I looked over the other entries regarding peak detection and none seem to answer my question.
I'm working with Fourier spectra of digitized audio that can't be measured again. There are no constraints on the nature of the audio.
Finding outliers is easy. I'm worried about "fat" peaks whose contours might be made jagged by background noise. Their "summits" are peaks among peaks. So how salient and separate does a peak need to be in order to qualify?
Is there a statistical way of approaching the problem? I could do something ad hoc, but without firm theoretical grounding, I rely much more on testing to confirm the algorithm's robustness. I'd like to know theoretically, rather than empirically, that my algorithm is sound.
Also, for those who have read this far, is there a good corpus of audio test data I can use for analysis algorithms?