Probability for Statistical Inference 1 (430-1-20)
Instructors
Miklos Zoltan Racz
Meeting Info
Lunt Hall 103: Tues, Thurs 2:00PM - 3:20PM
Overview of class
This course is the first in a three-quarter sequence of graduate probability theory with an eye towards statistical inference. It gives an introduction to mathematical probability theory, including measure theory, the law of large numbers, the central limit theorem, and related topics.
Registration Requirements
Math 320-1 (Real Analysis) and Statistics 420-1 (Introduction to Statistical Theory and Methodology 1) or equivalent.
Learning Objectives
The course is designed for PhD students whose ultimate research will involve rigorous mathematical probability, with a focus on statistical applications. The learning objectives are to develop a rigorous understanding of mathematical probability and to understand the deep connections between probability and statistics. Concretely, at the end of the course, students should be comfortable with measure theory (as it is used within probability theory), and they should understand and be able to use the law of large numbers and the central limit theorem.
Teaching Method
Interactive Lectures
Evaluation Method
Homework 30%, Midterm Exam 30%, Final Exam 40%
Class Materials (Required)
Probability Theory: lecture notes by Amir Dembo (for a similar course at Stanford), 2021. Freely available online: https://adembo.su.domains/stat-310c/lnotes.pdf
Class Materials (Suggested)
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. In particular, consider consulting:
- Probability: Theory and Examples (5th Edition) by R. Durrett, 2019. Freely available online: https://services.math.duke.edu/~rtd/PTE/pte.html
- Probability and Measure (3rd Edition) by P. Billingsley, 1995.
- Probability Theory: lecture notes by Terrence Tao. Freely available online: https://terrytao.wordpress.com/category/teaching/275a-probability-theory/
Class Notes
Please email the instructor with any questions.