Foundations of Computational Mathematics

, Volume 5, Issue 4, pp 389–407 | Cite as

Solving the Likelihood Equations

  • Serkan HostenEmail author
  • Amit KhetanEmail author
  • Bernd SturmfelsEmail author


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.

Maximum likelihood Maximum likelihood degree Syzygies Phylogenetic trees 


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Copyright information

© Society for Foundations of Computational Mathematics 2005

Authors and Affiliations

  1. 1.Department of Mathematics, San Francisco State University, San Francisco, CA 94132USA
  2. 2.Department of Mathematics, University of Massachusetts, Amherst, MA 01002USA
  3. 3.Department of Mathematics, University of California, Berkeley, CA 94720USA

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