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Markov Bases For Noncommutative Harmonic Analysis Of Partially Ranked Data, Ann Johnston
Markov Bases For Noncommutative Harmonic Analysis Of Partially Ranked Data, Ann Johnston
HMC Senior Theses
Given the result $v_0$ of a survey and a nested collection of summary statistics that could be used to describe that result, it is natural to ask which of these summary statistics best describe $v_0$. In 1998 Diaconis and Sturmfels presented an approach for determining the conditional significance of a higher order statistic, after sampling a space conditioned on the value of a lower order statistic. Their approach involves the computation of a Markov basis, followed by the use of a Markov process with stationary hypergeometric distribution to generate a sample.This technique for data analysis has become an accepted tool …