Course Announcement - Fall 2008

Math 239/Stat 260: Algebraic Statistics

Instructor: Bernd Sturmfels

Office hours: Wednesdays 9:00-11:00am and by appointment
Contact: bernd at math, 925 Evans, 642 4687

Time and Place: Tuesdays and Thursdays, 8:00-9:30pm, 81 Evans Hall

Prerequisites: Fluency in discrete probability and an interest in statistics. Knowledge of undergraduate abstract algebra (at the level of Math 113) and
computational algebra (at the level of the [Cox-Little-O'Shea]). Experience with mathematical software (Matlab, R, Maple, Magma, M2, etc.) will help.

Enrollment: This class is crosslisted and students can enroll either in Math 239 (CCN 54946) or in Stat 260 (CCN 87582).
Concurrent Courses: Please look at Math 143 (Elementary Algebraic Geometry) and the wide range of courses offered at Cal in statistics.
Objective: This crossdisciplinary class offers opportunity for graduate students with different backgrounds and interests to learn from each other.

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.