Statistics 210A: Theoretical Statistics (Fall 2023)

The Fall 2024 web site for this course is at https://stat210a.berkeley.edu/fall-2024/

If you are an undergraduate who wants to take the course, please fill out the permission code request form to let me know about your background.

Anyone considering taking the course is encouraged to read the frequently asked questions regarding preparation and review materials.

Course content

This is an introductory Ph.D.-level course in theoretical statistics. It is a fast-paced and demanding course intended to prepare students for research careers in statistics.

Statistics is the study of methods that use data to understand the world. Statistical methods are used throughout the natural and social sciences, in machine learning and artificial intelligence, and in engineering. Despite the ubiquitous use of statistics, its practitioners are perpetually accused of not actually understanding what they are doing. Statistics theory is, broadly speaking, about trying to understand what we are doing when we use statistical methods. See the course introduction for a more detailed explanation as well as comparisons to other Berkeley courses like Stat 215A and B, Stat 210B, and CS 281A/Stat 241A (Statistical Learning Theory).

Topics include: Statistical decision theory (frequentist and Bayesian), exponential families, point estimation, hypothesis testing, resampling methods, estimating equations and maximum likelihood, empirical Bayes, large-sample theory, high-dimensional testing, multiple testing and selective inference.

Course Information

• Prof. Will Fithian (Instructor)

  • 301 Evans

  • Office Hours: T 3:30-4:30 on Zoom, Th 9:30-10:30am in Evans 301

  • Email wfithian@berkeley.edu

• Taejoo Ahn (GSI)

  • Office Hours: W 9-10am on Zoom, F 12-1pm in Evans 444

  • Email

• Course schedule

  • Lectures TuTh 11-12:30, Evans 60

  • Recitation sections every second F 11am-12pm in Evans 344, beginning September 1

  • Final Exam Review TBD

  • Final Exam Wed December 13, 8-11am

• Lecture videos and homework solutions at bCourses

• Email policy: You can email me or the GSIs about administrative questions, with “[Stat 210A]” in the subject line. No math over email, please.

• Ed for announcements and technical discussion (no homework spoilers!)

• Gradescope for turning in homework

Materials

Handwritten lecture notes (Fall 2023):

• Lecture 1 (8-24-2023)

• Lecture 2 (8-29-2023)

• Lecture 3 (8-31-2023)

• Lecture 4 (9-5-2023)

• Lecture 5 (9-12-2023)

• Lecture 6 (9-14-2023)

• Lecture 7 (9-19-2023)

• Lecture 8 (9-21-2023)

• Lecture 9 (9-26-2023)

• Lecture 10 (9-28-2023)

• Lecture 11 (10-3-2023)

• Lecture 12 (10-5-2023)

• There is no Lecture 13

• Lecture 14 (10-10-2023)

• Lecture 15 (10-12-2023)

• Lecture 16 (10-17-2023)

• Lecture 17 (10-19-2023)

• Lecture 18 (10-26-2023)

• Lecture 19 (11-02-2023)

• There is no Lecture 20

• Lecture 21 (11-07-2023, 11-09-2023)

• There is no Lecture 22

• Lecture 23 (11-21-2023)

• There is no Lecture 24

• Lecture 25 (11-23-2021, 11-30-2021)

Typed lecture notes with additional detail (Fall 2023):

• Course introduction

• Measure theory basics

• Statistical models and estimation

• Exponential families

• Sufficiency

Materials from class:

• Exponential tilting demo (source)

• Demo of Bayesian inference for the beta-binomial distribution

• Demo of Gibbs sampler for Bayesian inference using JAGS

Assignments:

• Not Due Aug 30: Optional Homework 0 (source)

• Due Sep 6: Homework 1 (source)

• Due Sep 13: Homework 2 (source)

• Due Sep 20: Homework 3 (source)

• Due Sep 27: Homework 4 (source)

• Due Oct 4: Homework 5 (data for Problem 5) (source)

• Due Oct 11: Homework 6 (source)

• Due Thursday Oct 19: Homework 7 (source)

• Due Oct 25: Homework 8 (source)

• Due Nov 2: Homework 9 (source)

• Due Nov 8: Homework 10 (source) (data for Problem 4)

• Due Nov 15: Homework 11 (source)

• Optional: Homework 12 (source)

References

All texts are available online from Springer Link.

Main text:

• Keener, Theoretical Statistics: Topics for a Core Course, Springer 2010.

Supplementary texts:

• Lehmann and Casella, Theory of Point Estimation, Springer 1998.

• Lehmann and Romano, Testing Statistical Hypotheses, Springer 2005.

• Candes, Stats 300C Lecture notes, Stanford 2016.

• Unofficial Fall 2017 lecture notes (transcribed by student Sinho Chewi).

• Gelman & Hill, Data Analysis Using Regression and Multilevel/Hierarchical Models (for applied context).

Undergrad-level review texts for prerequisites:

• Axler, Linear Algebra Done Right, Chapters 1-3, 5-6.

• Abbott, Understanding Analysis, Chapters 1-3.

• Adhikari & Pitman, Probability for Data Science, Chapters 1-6, 8-9, 13-17, and 23.

Grading

Your final grade is based on:

• Weekly problem sets: 50%

• Final exam: 50%

Lateness policy: Homework must be submitted to Gradescope at midnight on Wednesday nights. Late problem sets will not be accepted, but we will drop your lowest two grades.

Collaboration policy: For homework, you are welcome to work with each other or consult articles or textbooks online, with the following caveats:

1. You must write up your solution by yourself.

2. You may NOT consult any solutions from previous iterations of this course.

3. If you collaborate or use any resources other than course texts, you must acknowledge your collaborators and the resources you used.

Academic integrity: You are expected to abide by the Berkeley honor code. Violating the collaboration policy, or cheating in any other way, will result in a failing grade for the semester and you will be reported to the University Office of Student Conduct.

Accommodations

Students with disabilities: Please see me as soon as possible if you need particular accommodations, and we will work out the necessary arrangements.

Scheduling conflicts: Please notify me in writing by the second week of the term about any known or potential extracurricular conflicts (such as religious observances, graduate or medical school interviews, or team activities). I will try my best to help you with making accommodations, but cannot promise them in all cases. In the event there is no mutually-workable solution, you may be dropped from the class.

Lecture schedule