We have an image analysis pipeline at work and one part of it involves peak detection. The peak detection algorithm we were using worked for normal data. One day a scientist came to me with data that was abnormal in that it had peaks with a high dynamic range, which failed given the current algorithm.

I thought about it a bit and was able to come up with a non-parametric test of randomness that detected whether a sequence of data was probably random or structured and it was able to detect not only the usual, large peaks but also those that were very small.

The reason I was really please with the result is that it was a case of applying a little thought to the problem, getting a nice probabilistic theory in place, and the resulting code was so straight forward and performant that it looked like a simplistic hack!