Statistics 210A: Theoretical Statistics (Fall 2020)

Announcement for undergraduates: 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.

Please note that due to the pandemic there is more uncertainty than usual in Fall 2020 about how many students we will be able to accommodate.

Course Information

• Prof. Will Fithian (Instructor)

  • 301 Evans

  • Office Hours: TBD

  • Email wfithian@thisschool.edu

• Tae Joo Ahn (GSI)

  • Office Hours: TBD

  • Email taejoo_ahn@thisschool.edu

• Lectures TuTh 9:30-11, 160 Kroeber

• Final Exam Tu Dec 15, 3-6pm

• Syllabus

• Announcements, handouts 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.

• Piazza for technical questions (no homework spoilers!)

• Gradescope for turning in homework

Materials

Lecture notes:

• Lecture 1 (8-29)

• Lecture 2 (9-3)

• Lecture 3 (9-5)

• Lecture 4 (9-10)

• Lecture 5 (9-12)

• Lecture 6 (9-17)

• Lecture 7 (9-19)

• Lecture 8 (9-24)

• Lecture 9 (9-26, 10-1)

• Lecture 10 (10-3)

• Lecture 11 (10-8)

• Lecture 12 (10-15)

• Lecture 13 (10-17)

• Lecture 14 (10-22, 10-24)

• Lecture 15 (10-29, 10-31)

• Lecture 16 (11-5)

• Lecture 17 (11-7)

• Lecture 18 (11-12, 11-14)

• Lecture 19 (11-19)

• Lecture 20 (11-21, 11-26)

• Lecture 21 (12-3)

Recitation section materials:

• Recitation 1 (9-19)

• Recitation 2

• Recitation 3 (see Ch. 3)

• Recitation 5 (11-12)

Materials from class:

• Exponential tilting demo (source)

• Demo of Bayesian inference for the beta-binomial distribution

• Bootstrap CI demo

Assignments:

Relevant articles:

• Completeness, Similar Regions, and Unbiased Estimation-Part I (Lehmann & Scheffé, 1950). In which completeness is introduced.

• The Circus Example (Basu, 1971). An amusing story about unbiased estimation.

• Why Isn't Everyone a Bayesian? (Efron, 1986). Concerning practical drawbacks of the Bayesian approach.

• Objections to Bayesian Statistics (Gelman, 2008) (with discussion and rejoinder). Common objections to Bayesian statistics and rebuttals to them.

Content

Stat 210A is Berkeley's introductory Ph.D.-level course on theoretical statistics. It is a fast-paced and demanding course intended to prepare students for research careers in statistics.

Topics:

• 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

Prerequisites:

• Linear algebra

• Real analysis

• One year of upper-division probability and statistics

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)

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