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Solving the Likelihood Equations

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, San Francisco State University, San Francisco, CA 94132, USA

    Serkan Hosten

  2. Department of Mathematics, University of Massachusetts, Amherst, MA 01002, USA

    Amit Khetan

  3. Department of Mathematics, University of California, Berkeley, CA 94720, USA

    Bernd Sturmfels

Authors
  1. Serkan Hosten
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  2. Amit Khetan
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  3. Bernd Sturmfels
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Corresponding authors

Correspondence to Serkan Hosten, Amit Khetan or Bernd Sturmfels.

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Hosten, S., Khetan, A. & Sturmfels, B. Solving the Likelihood Equations. Found Comput Math 5, 389–407 (2005). https://doi.org/10.1007/s10208-004-0156-8

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  • DOI: https://doi.org/10.1007/s10208-004-0156-8

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