STAT 430-1: Probability for Statistical Inference 1, Fall 2024
Basic info
Course description: This course is the first in a three-quarter sequence of graduate probability theory with an eye towards statistical inference.
This course covers an introduction to mathematical probability theory, including measure theory, the law of large numbers, and the central limit theorem, together with statistical applications.
Prerequisites: Undergraduate probability and familiarity with real analysis.
Instructor: Miklos Z. Racz
Lecture time and location: TuTh 2:00 - 3:20 pm, Lunt Hall 103
Office hours: Th 8 - 9 am and 3:30 - 4:30 pm, 2006 Sheridan Rd, Room 108
Teaching Assistant:
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Samuel Ozminkowski
Office hours: Tu 11:30 am - 1:30 pm, 2006 Sheridan Rd, Basement Room
Grading and course policies
Grading: There will be homework problem sets throughout the quarter (approximately weekly), as well as a midterm and a final exam.
Your final score is a combination of your performance in these, with the following breakdown:
- HW 30%
- midterm 30%
- final 40%
Final info: TBD
Homework and collaboration policy:
Please be considerate of the grader and write solutions neatly. Unreadable solutions will not be graded.
Please write your name, Northwestern email, and the names of other students you discussed with on the first page of your HW.
No late homework will be accepted. Your lowest homework score will be dropped.
You should first attempt to solve homework problems on your own.
You are encouraged to discuss any remaining difficulties in study groups of two to four people.
However, you must write up the solutions on your own and you must never read or copy the solutions of other students.
Similarly, you may use books or online resources to help solve homework problems, but you must always credit all such sources in your writeup, and you must never copy material verbatim.
Advice: do the homeworks! While homework is not a major part of the grade, the best way to understand the material is to solve many problems. In particular, the homeworks are designed to help you learn the material along the way.
Resources
We will provide hand-written course notes. In addition, we recommend consulting various textbooks that can aid in your learning. There are many texts that cover first year graduate probability. While the focus and scope of this course is slightly different, these texts can be valuable resources. David Aldous has an extensive annotated list here and here; in particular, consider consulting:
- A. Dembo, Lecture notes (for a similar course at Stanford), 2021. [ online ]
- R. Durrett, Probability: Theory and Examples (5th Edition), 2019. [ online ]
- P. Billingsley, Probability and Measure (3rd Edition), 1995.
Schedule
Tentative schedule and outline of topics covered:
- Lecture 1 (Sep 24): Introduction and overview.
- Lectures 2 -- 7 (Sep 26 -- Oct 15): Measure theory basics.
- Lecture 8 (Oct 17): Basic inequalities, concentration inequalities. Weak law of large numbers (LLN).
- Lecture 9 (Oct 22): Almost sure convergence, Borel--Cantelli lemmas.
- Lectures 10 -- 11 (Oct 24 -- Oct 29): Strong law of large numbers (LLN).
- Oct 31: Midterm exam.
- Lectures 13 -- 15 (Nov 5 -- 12): Weak convergence.
- Lectures 16 -- 19 (Nov 14 -- 26): Central limit theorem (CLT).
- Dec 5: Review.
- Dec 10: Final exam.
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