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Solving the likelihood equations. (English) Zbl 1097.13035
Summary: Given a model in algebraic statistics and data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying the local maxima in the probability simplex. Applications include models specified by rank conditions on matrices and the Jukes-Cantor models of phylogenetics. The maximum likelihood degree of a generic complete intersection is also determined.

MSC:
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
62F10 Point estimation
14P25 Topology of real algebraic varieties
62P10 Applications of statistics to biology and medical sciences; meta analysis
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