Solving the likelihood equations

Foundations of Computational Mathematics

Volumn 5, Issue 4, 2005, Pages 389-407

  Hoşten, Serkan ^a   Khetan, Amit ^b   Sturmfels, Bernd ^c  

^a SAN FRANCISCO STATE UNIVERSITY   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Maximum likelihood; Maximum likelihood degree; Phylogenetic trees; Syzygies

Indexed keywords

ALGEBRAIC ALGORITHMS; ALGEBRAIC STATISTICS; COMPLETE INTERSECTION; LIKELIHOOD EQUATION; LIKELIHOOD FUNCTIONS; PHYLOGENETIC TREES; RANK CONDITION; SYZYGIES;

COMPUTATIONAL METHODS; MAXIMUM LIKELIHOOD;

ALGEBRA;

EID: 31844444234     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-004-0156-8     Document Type: Conference Paper

References (16)

1. M. Bout and D. Richards, Counting and locating the solutions of polynomial systems of maximum likelihood equations, J. Symbolic Comput., to appear.
2. D. Bryant, Probabilistic models for splits graphs, Lecture at the Conference Phylogenetic Combinatorics and Applications, Uppsala, July 2004.
3. F. Catanese, S. Hoşten, A. Khetan, and B. Sturmfels, The maximum likelihood degree, Am. J. Math., to appear.
4. B. Chor, M. Hendy, and S. Snir, Maximum likelihood Jukes-Cantor triplets: Analytic solutions, Manuscript, August 2004.
5. B. Chor, B. Holland, D. Penny, and M. Hendy, Multiple maxima of likelihood in phylogenetic trees: An analytic approach, Molecular Biol. Evolution 17 (2000), 1529-1541.
6. B. Chor, A. Khetan, and S. Snir, Maximum likelihood on four taxa phylogenetic trees: Analytic solutions, The 7th Annual Conference on Research in Computational Molecular Biology - RECOMB 2003, Berlin, April 2003, pp. 76-83.
7. D. Cox, J. Little, and D. O'Shea, Using Algebraic Geometry, Graduate Texts in Mathematics, Vol. 185, Springer-Verlag, New York, 1998.
8. J. Felsenstein, Inferring Phylogenies, Sinauer Associates, Sunderland, UK, 2003.
9. W. Fulton, Intersection Theory, Springer-Verlag, New York, 1984.
10. D. Geiger, C. Meek, and B. Sturmfels, On the toric algebra of graphical models, Ann. Statist., to appear.
11. D. Grayson and M. Stillman, MACAULAY 2, A Software System for Algebraic Geometry, http://www.math.uiuc.edu/Macaulay2/.
12. G.-M. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, Springer-Verlag, New York, 2002.
13. 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.
14. J. Nocedal and S. J. Wright, Numerical Optimization, Springer-Verlag, New York, 1999.
15. R. Sainudiin, Enclosing the maximum likelihood of the simplest DNA model evolving on fixed topologies: Towards a rigorous framework for phylogenetic inference, Cornell University, 2004, BSCB Department, Technical Report BU-1653-M.
16. B. Sturmfels and S. Sullivant, Toric ideals of phylogenetic invariants, J. Comput. Biol, 12 (2005), 204-228.