algstat561

Course notes / topics

This page keeps track of course notes, material covered, homework schedule, and other relevant links. Unlike the static course homepage, this one is updated weekly.

• Most lectures use slides in the beginning, but I always also write on the board to supplement examples.
• It is impossible to follow the course only by reading these slides; students are expected to attend the lectures as well.
• All course communication, updates, announcements, logistics, and grading takes place on our Canvas course page.

Week 1 - invitation to algebraic statistics

• lecture 1 slides PDF
  • Additional notes on reasoning with data are written live.
  • notes version of the slides above <– same content as slides
• lecture 2 content & plan
  • additional examples shown in the lecture: biased coin, 3-way-independence

Homework 1 assigned. due 1/27/2026

Week 2 - statistical models, independence, and notation

• lecture 3 slides PDF * In-class worksheet 1
  • About Sampling Distributions
  • About marginalizing - additional notes
• Lecture 4 slides PDF
  • In-class worksheet 2 – may begin working on this, may take longer than one lecture.

Week 3 - algebraic varieties (what polynomials define), and basic computations

• lecture 5a slides PDF
  • Make sure you read Chapter 3 [the algebra primer], focusing on sections 3.1 and 3.2. I will go over some of these in class this week!
• lecture 6 slides PDF

Week 4 - Statistics primer intro to MLE

• lecture 7
  • including related book readings here
• MLE for the model of independence of 2 random variables
  • Student (Solomon) finishes the previous lecture by presenting the MLE for the independence model of 2 random variables. notes

Homework 2 assigned. due 2/19/2026

Week 5

• lecture 8
• lecture 9

Week 6

• In-class worksheet 3, finish at home.

What are ideals used for, actually? And examples to complete last week.

• lecture 10
• lecture 11
  • there’s an interlude on likelihood inference w/ Lagrange multipliers here

Week 7

Exact testing for discrete exponential families.

• lecture 12
• lecture 13

Week 8

• On the first day, we discussed your solutions to Homework set 2!
• On the second day, we defined Markov bases, discussed the Fundamental Theorem, some basic implications, and some examples of computing from Worksheets & homework. lecture 14

Homework 3 assigned. due 3/24/2026

Week 9

• In-class worksheet 4, finish at home. I should have posted this last week!

Are there any other issues with contingency tables we need to worry about?

• Cell bounds and disclosure limitation, lecture 15
• Sampling bounds and structural zeros

Homework 4 assigned. due 4/??/2026

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Appendix

What is this page?

Math 561 is a graduate-level course on algebraic and geometric methods in statistics. Course homepage is here, containing detailed info on the material, grading, etc.

Useful Info

Sample files: how to create your first .Rmd file! All of your HW can be submitted using markdown and html/pdf. Here are some templates I created for another course, just so you know what to expect:

• 514-hw-template.Rmd
• 514-hw-template.html
• 514-hw-template.pdf

Types of files

• html - course handouts.
• PDF - slides for short illustrations used within a live lecture
• Rmd - raw R Markdown code. This has two purposes: 1) for students to see how the basic output files are generated, and 2) to enable collaborators to make updates to the materials in future semesters.