Solving the Likelihood Equations
Abstract
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 JukesCantor models of phylogenetics. The maximum likelihood degree of a generic complete intersection is also determined.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2004
 arXiv:
 arXiv:math/0408270
 Bibcode:
 2004math......8270H
 Keywords:

 Mathematics  Statistics;
 Mathematics  Algebraic Geometry;
 Mathematics  Optimization and Control
 EPrint:
 20 pages