*The information contained on this website is for informational purposes only. The Undergraduate Record and Graduate Record represent the official repository for academic program requirements. These publications may be found at **http://records.ureg.virginia.edu/index.php*

**Program of Study**

The Department of Statistics administers programs leading to the degrees of Master of Science (M.S.) and Doctor of Philosophy (Ph.D.). These programs provide diverse opportunities for advanced study and research in all areas of applied and theoretical statistics, and practical experience in statistical consulting.

The Ph.D. program requires 44 hours of graded coursework, which includes all M.S.-level coursework and additional advanced theory and methodology courses, as well as courses that prepare the student for research.

The Ph.D. student must also pass a series of examinations that assess his or her ability to do research, culminating in the Ph.D. Final Exam, for which the student submits and presents a written dissertation prepared under the supervision of an advisor and committee of Statistics faculty members. The Ph.D. program is normally completed within five years.

**Overview of requirements**

The successful completion of the following courses and examinations are required for the Ph.D. in Statistics. They are described more fully below.

*Graded coursework requirements:*

- All in a list of lower-level required courses (9 credits)
- All in a list of advanced-level required courses (5 credits)
- At least six lower-level core elective courses (18 or more credits)
- At least two advanced-level core elective courses, one of which is in inference and one of which is in probability (6 credits)
- At least two free elective courses (6 or more credits)

*Pre-candidacy examination requirements:*

- Computer Skills Confirmation Test
- Ph.D. Qualifying Exam in Fundamental Knowledge
- Ph.D. Qualifying Exam in Research Skills

*Advanced examination requirements:*

- Ph.D. Preliminary Exam
- Ph.D. Final Exam

**Milestones**

The student becomes an “emerging candidate” for the Ph.D. upon passing the Computer Skills Confirmation Test, the Ph.D. Qualifying Exam in Fundamental Knowledge, and the Ph.D. Qualifying Exam in Research Skills.

The student becomes a “candidate” (or, informally, “full candidate”) for the Ph.D. upon completing all graded coursework requirements and passing the Ph.D. Preliminary Exam.

The Ph.D. student must successfully complete all pre-candidacy examinations and thus have reached the milestone of “emerging candidate” by the conclusion of the third year of study in order to proceed to the advanced examinations. He or she is also to have an Advisory Committee of four members, part of whose role is to set the requirements of each exam.

**Preparation **

Students should have 3 semester of calculus, linear algebra (comparable to UVA’s MATH 3351 or APMA 3080), and an introductory calculus-based probability and statistics course sequence, (comparable to MATH 3100/STAT 3120 or APMA 3100/3120). Most students find it extremely helpful to have an introductory real analysis course (“epsilon-delta proofs”) comparable to MATH 3310.

**Course requirements**

The Ph.D. program requires 72 credit hours of coursework. Among these, the Ph.D. student must take 44 credit hours of graded coursework stipulated as follows.

All of the following lower-level required courses:

- STAT 6120 (Linear Models),
- STAT 6190 (Introduction to Mathematical Statistics),
- STAT 7100 (Introduction to Advanced Statistical Inference).

All of the following advanced-level required courses:

- STAT 6510 (Skills in Statistical Research)
- STAT 6520 (Statistical Literature and Research Writing),\
- STAT 7200 (Introduction to Advanced Probability)

At least six lower-level core elective courses from the following list:

- STAT 5160/6160 (Experimental Design),
- STAT 5330 (Data Mining),
- STAT 6130 (Applied Multivariate Statistics),
- STAT 5140/6140 (Survival Analysis and Reliability),
- STAT 5170/6170 (Time Series Analysis),
- STAT 6020 (Optimization and Monte Carlo Methods in Statistics and Machine Learning)
- STAT 6260 (Categorical Data Analysis),
- STAT 6250 (Longitudinal Data Analysis),
- STAT 5390/6390 (Exploratory Data Analysis),
- STAT 5430/6430 (Statistical Computing),
- STAT 6440 (Bayesian Methods),
- STAT 5630/6630 (Statistical Machine Learning),
- STAT 5180/7180 (Survey Sampling Methods), and
- STAT 7130 (Generalized Linear Models)

Both of two advanced-level core elective courses:

- STAT 7510 (Advanced Inference) and
- STAT 7520 (Advanced Probability);

At least two free elective courses the following list:

- STAT 5310 (Clinical Trials),
- STAT 5265 (Investment Science I),
- STAT 5266 (Investment Science II),
- STAT 5340 (Bootstrap and Other Resampling Methods),
- STAT 5559 (Modeling in Biology and Medicine),
- STAT 8320 (Topics in Biostatistics),
- or any from the list of lower-level core elective courses.

Other graduate-level, three-credit courses from statistics or another department may substitute as a free elective course, subject to approval by the Director of Graduate Studies. Duplications are not allowed between 5000- and 6000-level versions of the same topic.

**Pre-Candidacy Examination Schedule**

* Computer Skills Confirmation Test: *The purpose of the Computer Skills Confirmation Test is to assess whether the student is prepared for hands-on, data-intensive study of statistical methodology and applications, especially regarding the use of statistical software. The content is elementary data set management and elementary statistical analysis applications using SAS and R. The student is presented with a problem whose solution requires substantial manipulation of a large or complicated data set. This is a written exam whose format is timed and open-book; the student’s solution would consist of written comments, computer code, and possibly printouts of graphics and statistical output. The exam is offered at least once per year, near the end of the Fall or Spring semester.

Every student is expected to take the Computer Skills Confirmation Test in the first semester of the program. Any student who does not take or pass the exam in the first semester is put on academic probation. A student who fails the Computer Skills Confirmation Test may sit for the test again at the discretion of the faculty.

* Ph.D. Qualifying Exam in Fundamental Knowledge: *The purpose of the Ph.D. Qualifying Exam in Fundamental Knowledge is to assess whether the student is prepared to develop theory and methodology in statistical research. The content of the exam matches topics in linear models, probability, and statistical inference that are typically covered in STAT 6120, STAT 6190, and STAT 7100. In its regular format, it is a timed, closed-book, written exam, to which the student is allowed to bring a formula sheet. The exam is offered once per year in this format, near the end of the first term of the summer session. A student who fails the Qualifying Exam in Fundamental Knowledge in its regular (written) format may request a new attempt of the exam in an oral format.

The Ph.D. student may take the PhD Qualifying Exam in Fundamental Knowledge at most twice, unless granted an exception by the Statistics Faculty.

* Ph.D. Qualifying Examination in Research Skills: *The purpose of the Ph.D. Qualifying Examination in Research Skills is to assess whether the student is prepared to carry out statistical research in two aspects: (i.) Is the student suitably prepared to work with data and apply statistical methodology toward a specific research goal? (ii.) Is the student suitably prepared to report his or her research contributions in publication-quality document?

The student must submit a paper that describes an interesting data set and related specialized area of research. The paper reviews literature and discusses potential research problems raised by the data or literature. The paper is expected to be of publishable quality; i.e., well written and properly formatted in the manner of a publication in the statistics literature. All or part of the paper may serve doubly to fulfill all or part of the requirements of STAT 6510, STAT 6520, or the Ph.D. Preliminary Exam.

The exam is intended to coordinate with the course sequence STAT 6510 (Skills in Statistical Research) and STAT 6520 (Statistical Literature). The timing of the exam and associated courses is as follows: In the third semester the student is to enroll in a section of STAT 6510. In the fourth semester, the student is to enroll in STAT 6520. The exam is taken at the end of the fourth semester.

**Advanced Examination Schedule**

* Ph.D. Preliminary Exam: *The purpose of this exam is to assess whether the candidate has identified a research topic and plan for its development that is likely to result in a successful Ph.D. Final Exam. The format of the Ph.D. Preliminary Exam is a private, two-hour oral exam, presented to the candidate’s Advisory Committee. The traditional requirement is that the candidate is to either defend a dissertation prospectus, or give a talk about existing developments in his or her research area, and then submit to questioning afterward.

The Ph.D. student must pass the Ph.D. Preliminary Exam before the start of his or her fifth year. They may take this portion of the exam at most twice.

* Ph.D. Final Exam: *The purpose of this exam is to assess whether the candidate has been successful as a researcher, scholar, and an academic. The criteria to be considered are as follows: (i.) Has the candidate made an original research contribution? (ii.) Has the candidate produced scholarship at a level consistent with the standards of the statistics discipline? (iii.) Has the candidate achieved skills with which to engage in academic discussion? The Ph.D. Final Exam consists of two components, a written dissertation and a dissertation defense. The dissertation defense is in the format of a three-hour oral exam, consisting of a public portion (of at least one hour in length) and a private portion, presented to the Advisory Committee. The requirement is almost always that the candidate is to present the contributions of the written dissertation, and then submit to questioning afterward.

A candidate who fails the Ph.D. Final Exam cannot retake the exam, and is dismissed from the program.