Statistics 210A: Theoretical Statistics (Fall 2020)
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 Information
Prof. Will Fithian (Instructor)
Tae Joo Ahn (GSI)
Forest Yang (GSI)
Course schedule (Google Calendar link):
Lectures TuTh 9:30-11
Recitation sections every second F 4pm beginning September 4
Happy hours F 4-5pm on off weeks
Final Exam Review F Dec 11, 4pm
Final Exam Tu Dec 15 (take-home)
Zoom links:
Syllabus
Lecture videos and 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 announcements and technical questions (no homework spoilers!)
Gradescope for turning in homework
Link to Google calendar for course
Materials
Lecture notes:
Lecture 1 (8-27-2020)
Lecture 2 (9-1-2020)
Lecture 3 (9-3-2020)
Lecture 4 (9-8, 9-10-2020)
Lecture 5 (9-10-2020, 9-15-2020)
Lecture 6 (9-15-2020)
Lecture 7 (9-17-2020)
Lecture 8 (9-22-2020)
Lecture 9 (9-24-2020, 9-29-2020)
Lecture 10 (9-29-2020, 10-1-2020)
Lecture 11 (10-6-2020)
There is no Lecture 12
Lecture 13 (10-8-2020)
Lecture 14 (10-13-2020)
Lecture 15 (10-15-2020, 10-20-2020)
There is no Lecture 16
Lecture 17 (10-22-2020)
Lecture 18 (10-27-2020, 10-29-2020)
There is no Lecture 19
Lecture 20 (11-03-2020)
Lecture 21 (11-05-2020, 11-10-2020)
There is no Lecture 22
Lecture 23 (11-12-2020, 11-17-2020)
There is no Lecture 24
Lecture 25 (11-19-2020, 11-24-2020)
Multiple testing lecture (12-01-2020, 12-03-2020)
Causal inference lecture (12-08-2020, 12-10-2020)
Materials from class:
Assignments:
Relevant articles:
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
References
All texts are available online from Springer Link.
Main text:
Supplementary texts:
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: 80%
Final exam: 20%
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:
You must write up your solution by yourself.
You may NOT consult any solutions from previous iterations of this course.
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
Date | Reading | Topic |
Aug. 27 | Chap. 1 and Sec. 3.1 of Keener | Probability models and risk |
Sep. 1 | Chap. 2 of Keener | Exponential families |
Sep. 3 | Chap. 2 and Sec. 3.2 of Keener | Sufficient statistics |
Sep. 8 | Secs. 3.4, 3.5, and 3.6 of Keener | Minimal sufficiency and completeness |
Sep. 10 | Secs. 3.6 and 4.1 of Keener | Rao-Blackwell theorem |
Sep. 15 | Secs. 4.1 and 4.2 of Keener | UMVU estimation |
Sep. 17 | Secs. 4.5 and 4.6 of Keener | Information inequality |
Sep. 22 | Secs. 7.1 and 7.2 of Keener | Bayesian estimation |
Sep. 24 | Secs. 7.1 and 7.2 of Keener | Conjugate priors |
Sep. 29 | Secs. 7.2 and 11.1 of Keener | More on Bayes |
Oct. 1 | Secs. 7.2 and 11.1 of Keener | Hierarchical priors, empirical Bayes |
Oct. 6 | Secs. 11.1, 11.2 and 9.4 of Keener | James-Stein paradox, confidence intervals |
Oct. 8 | Secs. 5.1 and 5.2 of Lehmann-Casella | Minimaxity and admissibility |
Oct. 13 | Secs. 12.1, 12.2, 12.3 and 12.4 of Keener | Hypothesis testing, Neyman-Pearson lemma |
Oct. 15 | Secs. 12.3, 12.4, 12.5, 12.6 and 12.7 of Keener | UMP tests |
Oct. 20 | Secs. 13.1, 13.2, and 13.3 of Keener | Testing with nuisance parameters |
Oct. 22 | Secs. 13.1, 13.2, and 13.3 of Keener | UMP unbiased tests |
Oct. 27 | Secs. 13.1, 13.2, and 13.3 of Keener | UMP unbiased tests |
Oct. 29 | Secs. 14.1, 14.2, 14.4, 14.5, and 14.7 of Keener | Linear models |
Nov. 3 | Secs. 8.1, 8.2, and 8.3 of Keener | Asymptotic concepts |
Nov. 5 | Secs. 8.3 and 8.4 of Keener | Maximum likelihood estimation |
Nov. 10 | Secs. 8.5, 9.1, and 9.2 of Keener | Relative efficiency |
Nov. 12 | Secs. 9.1, 9.2, and 9.3 of Keener | Consistency of the MLE |
Nov. 17 | Secs. 9.1, 9.2, and 9.3 of Keener | Asymptotic normality of MLE |
Nov. 19 | Secs. 9.5 and 9.7 of Keener | Trio of asymptotic likelihood-based tests and CIs |
Nov. 24 | Secs. 19.1-19.3 of Keener | Bootstrap and permutation tests |
Nov. 26 | | No class (Thanksgiving) |
Dec. 1 | 15.1-15.4 of Lehmann-Romano | Bootstrap theory |
Dec. 3 | Lecs. 2, 3 of Candes | Testing in high dimensions |
Dec. 8 | Lec. 6 of Candes | Multiple testing |
Dec. 10 | Lecs. 8 and 9 of Candes | Multiple testing |
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