computational algebra (at the level of the [Cox-Little-O'Shea]). Experience with mathematical software (Matlab, R, Maple, Magma, M2, etc.) will help.

**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.