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We develop a probabilistic algorithm for computing elimination ideals of likelihood equations. We show experimentally that it is far more efficient than directly computing Groebner bases or the interpolation method for medium to large size models. Furthermore, we deduce discriminants of the elimination ideals, which play a central role in real root classification. In particular, we can compute the discriminant of one Jukes-Cantor model in phylogenetics (with size 8 GB text file).

A New Method for Computing Elimination Ideals of Likelihood Equations