article

Solving the Likelihood Equations

Authors:

Bernd SturmfelsAuthors Info & Claims

Foundations of Computational Mathematics, Volume 5, Issue 4

Pages 389 - 407

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

Published: 01 November 2005 Publication History

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.

References

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B. Chor, M. Hendy, and S. Snir, Maximum likelihood Jukes--Cantor triplets: Analytic solutions, Manuscript, August 2004.

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Digital Library

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G.-M. Greuel, G. Pfister, and H. Schönemann, SINGULAR 2.0, A Computer Algebra System for Polynomial Computations, University of Kaiserslautern, 2001, http://www.singular.uni-kl.de.

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Cited By

Hill MRodriguez J(2024)A Maximum Likelihood Estimator for Quartets under the Cavender-Farris-Neyman ModelACM Communications in Computer Algebra10.1145/3712023.371202858:2(35-38)Online publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1145/3712023.3712028
Härkönen MHollering BKashani FRodriguez J(2020)Algebraic optimization degreeACM Communications in Computer Algebra10.1145/3427218.342722254:2(44-48)Online publication date: 29-Sep-2020
https://dl.acm.org/doi/10.1145/3427218.3427222
Tang Xde Wolff TZhao RDavenport JWang DKauers MBradford R(2019)A New Method for Computing Elimination Ideals of Likelihood EquationsProceedings of the 2019 International Symposium on Symbolic and Algebraic Computation10.1145/3326229.3326241(339-346)Online publication date: 8-Jul-2019
https://dl.acm.org/doi/10.1145/3326229.3326241
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Solving the Likelihood Equations
1. Theory of computation

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cover image Foundations of Computational Mathematics

Foundations of Computational Mathematics Volume 5, Issue 4

November 2005

139 pages

ISSN:1615-3375

EISSN:1615-3383

Issue’s Table of Contents

Copyright © Copyright © 2005 Society for Foundations of Computational Mathematics.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 November 2005

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Cited By

Hill MRodriguez J(2024)A Maximum Likelihood Estimator for Quartets under the Cavender-Farris-Neyman ModelACM Communications in Computer Algebra10.1145/3712023.371202858:2(35-38)Online publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1145/3712023.3712028
Härkönen MHollering BKashani FRodriguez J(2020)Algebraic optimization degreeACM Communications in Computer Algebra10.1145/3427218.342722254:2(44-48)Online publication date: 29-Sep-2020
https://dl.acm.org/doi/10.1145/3427218.3427222
Tang Xde Wolff TZhao RDavenport JWang DKauers MBradford R(2019)A New Method for Computing Elimination Ideals of Likelihood EquationsProceedings of the 2019 International Symposium on Symbolic and Algebraic Computation10.1145/3326229.3326241(339-346)Online publication date: 8-Jul-2019
https://dl.acm.org/doi/10.1145/3326229.3326241
Hauenstein JRodriguez JSottile F(2018)Numerical Computation of Galois GroupsFoundations of Computational Mathematics10.5555/3269376.326942418:4(867-890)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.5555/3269376.3269424
Horobeź ERodriguez J(2017)The maximum likelihood data singular locusJournal of Symbolic Computation10.1016/j.jsc.2016.08.00779:P1(99-107)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.jsc.2016.08.007
Martín del Campo ARodriguez J(2017)Critical points via monodromy and local methodsJournal of Symbolic Computation10.1016/j.jsc.2016.07.01979:P3(559-574)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.jsc.2016.07.019
Draisma JHorobeţ EOttaviani GSturmfels BThomas R(2016)The Euclidean Distance Degree of an Algebraic VarietyFoundations of Computational Mathematics10.1007/s10208-014-9240-x16:1(99-149)Online publication date: 1-Feb-2016
https://dl.acm.org/doi/10.1007/s10208-014-9240-x
Guo FSafey El Din MWang CZhi LRobertz DLinton SYokoyama K(2015)Optimizing a Parametric Linear Function over a Non-compact Real Algebraic VarietyProceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2755996.2756666(205-212)Online publication date: 24-Jun-2015
https://dl.acm.org/doi/10.1145/2755996.2756666
Rodriguez JTang XRobertz DLinton SYokoyama K(2015)Data-Discriminants of Likelihood EquationsProceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2755996.2756649(307-314)Online publication date: 24-Jun-2015
https://dl.acm.org/doi/10.1145/2755996.2756649
Rodriguez JZhi LWatt S(2014)Maximum likelihood for dual varietiesProceedings of the 2014 Symposium on Symbolic-Numeric Computation10.1145/2631948.2631959(43-49)Online publication date: 28-Jul-2014
https://dl.acm.org/doi/10.1145/2631948.2631959
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