PhD Coursework

This page gives an informal overview of typical classes taken by PhD graduate students in the department.

The structure of the Ph.D. was radically revamped in 2004. In particular, the decades-old preliminary exams were deprecated in favor of more holistic assessment methods.

The core courses are 205A and 205B (probability theory), 210A and 210B (theoretical statistics) and 215A and 215B (applied statistics). In addition, Ph.D. candidates will usually choose four first year courses from these six - often both parts of two of the three series 205, 210 and 215. There can be good reasons for not following this pattern: 

  • If you are interested in interdisciplinary work, you may wish to include a course from another department. 
  • If you have done graduate work at another university, the material in the "A" courses may already be familiar to you (or it may not.) Other courses may be more appropriate. 
  • You may come in to the program knowing that you wish to specialize in probability. After discussion with your graduate advisor it may be possible not to take any of 210A/B or 215A/B.

However, you will need to consult with the graduate advisor to receive approval.

All of the core courses require a large commitment of time, particularly with the homework. Taking more than two of them per semester (eight units) is a Herculean task. Everybody is required by the university to be enrolled in 12 units, but you can enroll in "filler" units to bring you up to this level. The department also offers courses beyond the core that are more research oriented. They complement the core courses and typically focus on reading and presenting papers, rather than weekly homework. Also, bear in mind that your thesis topic does not need to come from a general area covered by the courses you take in first year: some students who take 205 and 215 in their first year end up working on theoretical statistics, and so on.

Choosing your courses

Your first point of contact should be the Graduate or Masters advisor; see the contacts page on the department site for up-to-date information. Next, you should talk to current students, who tend to be more accurate judges of workloads than are professors. Professors can make recommendations about which classes may be useful for your particular research interests. 


Assessment 


Each course has its own assessment. Depending on the course, this may include problem sets, group projects, take-home and/or in-class midterms, and final exams. 

At the end of your first year, the Graduate Faculty Advisor will evaluate your coursework as a whole and decide whether you advance to the next stage of your graduate career.


Computing classes 


STAT 243 is an intensive course, designed to help students pick up some relevant programming skills. If you don't feel comfortable programming, you should consider taking this. In an applied course like STAT 215, there is a large computing component, and though the course GSI will give an introduction to the software required, students with limited statistical computing experience often find it difficult to pick up the software skills at the same time as the course material. 


Core Courses 


Stat 205: Probability Theory 


Rigorous and theoretical; a suitable course if your mathematical background is strong. Some knowledge of measure theory is extremely helpful: the basics of measure theory are covered in the first few weeks of lectures, but students who haven't seen it before often find this isn't enough. The homeworks given in this course are time-consuming and hard. Students often form study groups to share ideas. 

205A: Measure theoretical approach to probability, conditional expectation, martingales. 205B: Markov processes, limit theorems, characteristic functions, ergodic theory, brownian motion. 


Stat 210: Theoretical Statistics

210A contains essential material for the understanding of statistics. 210B contains more specialized material. The 210 courses are less mathematically rigorous than the 205 courses. 210A is easier than 205A; 210B is very difficult conceptually, though in practice it's easy to perform adequately. Homework is time-consuming.

210A: The frequentist approach to statistics with comparison to Bayesian and decision theory alternatives, estimation, model assessment, testing, confidence regions, some asymptotic theory. 210B: Depends on the lecturer, but focus is usually asymptotic theory.

Stat 215: Statistical Models: Theory and Application

There are computing/data analysis assignments as well as readings; sometimes there is additional homework. How these courses are run depend a lot on the instructor. Usually they are discussion-based.

215A: Exploratory techniques; critical readings of applied papers; overview of methods, including regression, testing, and resampling. 215B: Topics include advanced regression, causal inference, and optimization.


Other Regular Courses 

STAT 238 Bayesian Statistics 

STAT C239A and C239B The Statistics of Causal Inference in the Social Science 

STAT 240 Nonparametric and Robust Methods 

STAT 241A Statistical Learning Theory 

STAT 241B Advanced Topics in Learning and Decision Making 

STAT 243 Introduction to Statistical Computing 

STAT 244 Statistical Computing 

STAT 246 Statistical Genetics 

STAT 248 Analysis of Time Series 

STAT 251 Stochastic Analysis with Applications to Mathematical Finance 

STAT 259 Reproducible and Collaborative Statistical Data Science 

STAT 261 Quantitative/Statistical Research Methods in Social Sciences 

STAT 272 Statistical Consulting


Advanced Topic Courses

These courses are not taught regularly, and the content varies from semester to semester and by instructor. Topic announcements are usually made at the end of the preceding semester. These courses can be taken repeatedly for credit by graduate students, and the department encourages people to take these for credit in order to show the university that there really are people taking these courses. The three advanced topics course titles are: 

  • Stat 206: Stochastic Processes 
  • Stat 212: Topics in Theoretical Statistics 
  • Stat 260: Topics in Probability and Statistics
Recent examples include: 
  • Interacting Diffusions in Probability and Statistical Physics (Stat 206, Fall 2016, Hammond) 
  • Self-avoiding Walks (Stat 206, Spring 2016, Hammond) 
  • Topics on Deep Learning and High-dimensional Representation Learning (Stat 212, Spring 2016, Bruna) 
  • Convex Optimization and Approximation: Optimization for Modern Data Analysis (Stat 260, Spring 2016, Recht)

In addition, various individual study courses may be taken under the supervision of a faculty member, and some larger scale reading groups can be organized. For example, in Fall 2016 there's a reading group in modern causal inference in complex models.


Courses in Other Departments

Depending on your research interests, you may find courses outside the department to be beneficial.

The math department in particular offers a wide variety of courses, many of which are useful for probabilists, but there are also some relevant to theoretical statisticians. Some core mathematics courses which are particularly relevant for probabilists are Topology and Analysis (Math 202A/B), Partial Differential Equations (Math 222A/B) and Banach Algebras and Operator Theory (Math 206). Sometimes some of the Math 275 (special topics) courses may be worth looking at, particularly those with Prof. Rezakhanlou. 


Some students, particularly those interested in machine learning, also take courses in the computer science department, which offers a broad array of regular standard classes and advanced topics classes. More information here.


Seminars


The department runs many seminars. The main one is the Neyman seminar, from 4-5pm on Wednesdays in Evans 1011. 

Students are encouraged to enroll for credit in these seminars, particularly the Neyman and Probability seminars. Seminars are an important part of life in the department. They allow you to see how new theory is developed, and how existing theory is put into action. They also provide research topics and ideas, as well as sometimes providing delicious food.

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