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, 8:00-9:30am, 81 Evans Hall

Prerequisites: Fluency in discrete probability and an interest in statistics. Knowledge of 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 class offers an opportunity for graduate students with different backgrounds and interests to learn from each other.

Course text: Lectures on Algebraic Statistics by Mathias Drton, Seth Sullivant and myself.

Final Projects: Here are the term papers written by the students for this course:
Shuchao Bi: A Criterion for Tensor Rank
Dustin Cartwright: Discretizing Gaussian Models
Melody Chan: Tropical Decomposition of Symmetric Tensors
Angelica Cueto: Implicitization Challenge for Binary Factor Analysis
Alexander Fink: Primary Decomposition for the Intersection Axiom
Shaowei Lin: Asymptotic Approximation of Marginal Likelihood Integrals
Anna-Sapfo Malaspinas and Caroline Uhler: A Strategy for Detecting Multiple Trait Loci in Disease Association Studies
Adam Merberg: Maximum Likelihood Estimation on Determinantal Varieties
Joe Neeman: A Model for Biochemical Reaction Networks
Anne Shiu: Persistence of Deterministic Population Processes and the Global Attractor Conjecture (with David Anderson)
Cynthia Vinzant: Sparsity in Covariance Selection for Gaussian Graphical Models

Schedule of lectures:
August 28: An invitation to algebraic statistics
September 2: Independence and hypotheses testing (Section 1.1)
September 4: The many bases of a lattice (Section 1.3)
September 9: Hierarchical models (Section 1.2)
September 11: Likelihood inference for discrete models (Section 2.1)
September 16: Software day
September 18: Likelihood inference for Gaussian models (Section 2.1)
September 23: MLE for implicit models (Section 2.2)
September 27: Discrete CI models (Section 3.1)
September 30: Gaussian CI models (Section 3.1) and Erick Matsen
October 2: The intersection axiom (Section 6.6)
October 7: Graphical models (Section 3.2)
October 9: Hammersley-Clifford Theorem (Section 3.3)
October 14: Caroline Uhler and Anna-Sapfo Malaspinas
October 16: Open problems in algebraic statistics
October 21: Likelihood ratio tests (Section 2.3)
October 23: No class: please attend the lectures by Lior and Mathias.
October 28: Mixture models (Section 4.1)
October 30: Secant varieties (Section 4.1)
November 4: Factor analysis (Section 4.2)
November 6: Information criteria (Section 5.1)
November 11: No class (Veterans Day)
November 13: Marginal likelihood (Section 5.2, Shaowei)
November 18: Phylogenetics: The general Markov model
November 20: Generalized principal component analysis
November 25: Phylogenetics: Group-based models
November 27: No class (Thanksgiving)
December 2: Alex Fink and Joe Neeman
December 4: Shuchao Bi and Adam Merberg
December 9: Melody Chan and Angelica Cueto
December 10: Dustin Cartwright and Cynthia Vinzant
Dec 17 (at MSRI): Shaowei Lin
Dec 18 (at MSRI): Caroline Uhler

Homework: There will be regular assignments, posted here in pdf format, during the first eight weeks of the course.
Homework 1: due September 14
Homework 2: due September 23
Homework 3: due September 30
Homework 4: due October 14

Deadlines: The following dates are all Thursdays:
November 20: Preliminary Report is Due
December 10: Final Paper is Due

Grading: The course grade will be based on both the homework and the course projects.

MSRI Workshop:
Course participants are invited to participate in the Workshop on Algebraic Statistics at MSRI from December 15 to 18.

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.