Statistics and Computing by Counting Inversions

When data comes in the form of permutations, statisticians and computer scientists turn to combinatorics in order to analyze it.  I will describe how enumerative combinatorics, algorithms and statistics come together in this endeavor.

At the center of the results is the *code* of a permutation. This natural mathematical way to count the inversions in a permutation is key both to fast computing and to interpreting the models we use.

Joint work with: Annelise Wagner, Chris Meek, Harr Chen, Alnur Ali, Raman Arora,Brendan Murphy, Bhushan Mandhani, Le Bao, Kapil Phadnis, Arthur Patterson, and Jeff Bilmes.