Yale Statistics
Ph.D. Program

Revised: 24 November 2010
  Course of Study
  Teaching requirements
  SPEAK: a test of English proficiency
  Qualifying Examinations
  Prospectus and Dissertation
  Dissertation fellowships
  Further information

The Department offers a broad training program comprised of the main areas of statisical theory (with emphasis on foundations, Bayes theory, decision theory, nonparametric statistics), probability theory (stochastic processes, asymptotics, weak convergence), information theory, econometrics, classification, statistical computing, and graphical methods.

With this background, graduates of the program have found excellent positions in universities, industry, and government. Recent graduates have accepted appointments at the Duke University, University of California at Santa Barbara, The City University of New York, Yale University, Bristol-Meyers Squibb, RAND, Federal Reserve Board, New York University, Trinity University, Iowa State University, Merck, and Tulane University.


  • All applications for this program should be submitted directly to the Yale Graduate School Office of Admissions through the online application page.

  • Application requirements and guidelines
  • GRE scores for the General Test and for the Subject Test (usually in Mathematics, sometimes in the area of the undergraduate major) should accompany an application.
  • All applicants should have a strong mathematical background, including advanced calculus, linear algebra, elementary probability theory, and at least one course providing an introduction to mathematical statistics. An undergraduate major may be in statistics, mathematics, computer science, or in a subject in which significant statistical problems may arise.
  • For those whose native language is not English, the Test of English as a Foreign Language (TOEFL) scores are required.
  • The Ph.D. program admits only a small number of new students each year. Only 6 initial offers (for a pool of 73 applications) were made for admission in fall 2010.
  • The offer of admission typically includes full tuition and a stipend. Consult the Graduate School's financial assistance page for details.
  • Tuition and Living Costs
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Course of Study

All graduate students must consult at the start of each semester with the Director of Graduate Studies (DGS),
whose signature is needed before course selections beome official.
  • Fourteen courses are required before students can be admitted to candidacy after the second year.
    Usually students take four courses in each semester of the first year and three courses in each semester of the second year.
  • Ph.D. students are strongly advised to take the courses highlighted in RED, which are taught every year,
    even if they involve some review of material taken in undergraduate courses.
    Substitutions are possible with the permission of the DGS.
  • The theory qualifying exam is usually based on a combination of
    advanced undergraduate material (as covered in Stat 241, 242, and 251/551) and
    graduate material at the level of Stat 600, 610, and 612.
  • For the practical qualifying exam, students are expected to be comfortable with R, and have had experience at working with real data.
    Most students gain that experience from a combination of Stat 661, 625 and participation in the statistical consulting clinic (Stat 627).

Ph.D Fall Spring
first year Stat 610 (Statistical Inference)
Stat 612 (Linear Models)
Stat 661 (Data Analysis)
+ one more course, such as Real Analysis or Measure Theory from the Math Dept.
Often students also attend Stat 627 (1/2 credit) to gain experience with real data.
Stat 600 (Advanced Probability)
Stat 551 (Stochastic Processes)
+ two other courses, such as Stat 664 (Information Theory) or Stat 660 (Multivariate methods for the social sciences).
Also Stat 627 for the other 1/2 credit.
second year Stat 625 (Case Studies) required
+ two electives
Stat 626 (Practical work) required
+ two electives

The electives are often chosen from special topics courses that are offered on an irregular schedule,
determined by a combination of student demand and faculty interests.
See the course lists for typical offereings.

Normally during the first two years, fourteen term courses in this and other departments are taken to prepare students for research and practice of statistics. These include courses devoted to case studies and practical work, for which students prepare a written report and give an oral presentation. Specific course requirements.

There is no foreign language requirement.

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The SPEAK test

From the web page at http://www.yale.edu/eli/fall/speaktestinfo.html:
The SPEAK test is required for all international Ph.D. students who are non-native speakers of English. Students must score a 50 before being offered a TA position at Yale. Students who achieve less than 50 are considered for grading positions only.

For further details consult that web site.

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Teaching requirements

From the Graduate School's Programs and Policies [page 539]:
Because the Graduate School considers teaching experience to be an integral part of graduate education, doctoral students receive financial aid packages that include teaching fellowships. In many programs there are specific years when students are expected to teach. For example, most humanities and social science students will teach in their third and fourth years. In the natural sciences, the timing of teaching is earlier or is flexible across several years. When requested by the student for compelling academic reasons, these patterns may be adjusted with the permission of an associate dean and the director of graduate studies contingent on the student's satisfactory academic progress and on sufficient course enrollment.
See http://www.yale.edu/graduateschool/academics/program.html for details about the Teaching Fellow Program and the teaching requirement.

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Qualifying Examinations

Course work prepares students for a Ph.D. qualifying examination, which is usually taken after three semesters of study. The qualifying examination consists of three parts:

  1. Practical Exam: a written report on an analysis of a data set. Held during a five day period in December, following the end of classes.
  2. Theory Exam: a written paper on theoretical statistics. A one-day exam (9:00 am -- 4:00 pm) held in early January.
  3. Oral Exam: held shortly after completion of the Theory Exam.
All parts of the qualifying examination must be competed before beginning the third year.

  • A typical theory exam. [Look at http://www.stat.yale.edu/dept-private/Exams/ for copies of other old exams.Yale login required].

  • Well prepared students sometimes take one of the Practical or Theory Exams in their first year. No record is kept of an unsuccesful attempt.

  • Students who do not pass the exams during January/December of their second year have the option of a retake at the end of the spring semester.

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Prospectus and Dissertation

Dissertation research in collaboration with one member of the faculty is begun during the third year. A prospectus for the dissertation should be submitted no later than the first week of March in the third year. The prospectus must be accepted by the department before the end of the third year.

Upon successful completion of the qualifying examination and the prospectus (as well as meeting the Graduate School Honors requirements), the student is admitted to candidacy. Most students complete the dissertation in the fifth year.

Please see our Alumni page for a sampling of recent Dissertation topics.

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Dissertation fellowships

From the Graduate School's Programs and Policies [page 538]:
The Graduate School offers University Dissertation Fellowships as part of its five-year financial aid package to eligible advanced graduate students in the humanities and social sciences once they have advanced to doctoral candidacy. These awards are made when a student's adviser and director of graduate studies certify that the student will be engaged full-time in research and writing, is making satisfactory progress toward the degree, and has a reasonable schedule for the timely completion of the dissertation. The University Dissertation Fellowship is usually taken in consecutive terms (beginning in either the fall or spring term) and must be completed by the end of the sixth year of study. With the permission of the Graduate School, it may be interrupted in certain circumstances when recommended by the department. It may never be held concurrently with a teaching fellowship of any kind. Students who accept a teaching position in the fall or spring of the year of final eligibility will forfeit that term's dissertation fellowship amount. Prize dissertation fellowships awarded by the Graduate School, such as the Whiting and Leylan fellowships, replace the University Dissertation Fellowship. Students receiving external funding for dissertation research or writing may be eligible for a combined award and should consult the External Fellowships and Combined Award policy. Application materials and additional information can be obtained online at www.yale.edu/graduateschool/funding or from the appropriate associate dean.

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Further information

Consult the Graduate School's Programs and Policies for general information about Ph.D. study at Yale.

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