Markov bases for noncommutative Fourier analysis of ranked data
To calibrate Fourier analysis of S-5 ranking data by Markov chain Monte Carlo techniques, a set of moves (Markov basis) is needed. We calculate this basis, and use it to provide a new statistical analysis of two data sets. The calculation involves a large Grobner basis computation (45825 generators), but reduction to a minimal basis and reduction by natural symmetries leads to a remarkably small basis (14 elements). Although the Grobner basis calculation is infeasible for S-6, we exploit the symmetry of the problem to calculate a Markov basis for S-6 with 7,113,390 elements in 60 symmetry classes. We improve a bound on the degree of the generators for a Markov basis for S-n and conjecture that this ideal is generated in degree 3. (c) 2005 Elsevier Ltd. All rights reserved.
markov bases ranked data grobner bases