Mathematics – Commutative Algebra
Scientific paper
2004-05-04
Journal of Symbolic Computation, Volume 41, Issue 2, February 2006, Pages 182-195
Mathematics
Commutative Algebra
16 pages, 2 figures. To appear in the Journal of Symbolic Computation, special issue on Computational Algebraic Statistics. Mi
Scientific paper
10.1016/j.jsc.2005.04.009
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 Gr\"obner 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 Gr\"obner 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 58 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.
Diaconis Persi
Eriksson Nicholas
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