Markov bases for noncommutative Fourier analysis of ranked data

• Autores: Persi Diaconis, Nicholas Eriksson
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 2, 2006, págs. 182-195
• Idioma: inglés
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• Resumen

  • To calibrate Fourier analysis of S5 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 Gröbner 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 Gröbner basis calculation is infeasible for S6, we exploit the symmetry of the problem to calculate a Markov basis for S6 with 7,113,390 elements in 60 symmetry classes. We improve a bound on the degree of the generators for a Markov basis for Sn and conjecture that this ideal is generated in degree 3.