Solving the Likelihood Equations

Details Solving the Likelihood Equations Solving the Likelihood Equations

2004-08-19

arxiv.org/abs/math/0408270v2

Mathematics

Statistics Theory

20 pages

Scientific paper

Given a model in algebraic statistics and some 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.

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