Course text:
Lecture notes are posted here in pdf format:
Version of April 29, 2008.
These notes will be updated regularly.
Tentative Schedule:
Week 1: Two-way contingency tables
Week 2: Tools from algebra and geometry
Week 3: Design of experiments
Week 4: Multidimensional tables
Week 5: Toric models and Markov bases
Week 6: Maximum likelihood equations
Week 7: Graphical models
Week 8: Independence models
Week 9: Phylogenetic models
Week 10: Gaussians and semidefinite matrices
Week 11: Bayesian integrals
Week 12: Hidden variables and secants varieties
Week 13+: Student presentations
Homework:
There will be weekly homework during the
first eight weeks of the course.
Projects:
Research teams
consisting of two or three students will
work on a project related to algebraic statistics.
Grading:
The course grade will be based on both the homework
and the course projects.
Further Reading:
M. Drton and S. Sullivant:
Algebraic statistical models,
Statistica Sinica 17 (2007) 1273-1297.
L. Pachter and B. Sturmfels:
Algebraic Statistics for Computational
Biology, Cambridge University Press, 2005.
G. Pistone, E. Riccomagno and H. Wynn: Algebraic Statistics,
Chapman and Hall/CRC, Bocan Raton, 2000.
B. Sturmfels: Solving Systems of Polynomial Equations,
American Mathematical Society, 2002.