### Qualifying Requirements prior to Fall 2019

### Qualifying Exams

Doctoral students are required to pass two qualifying exams.

- Comprehensive theory exam. This exam covers probability and theoretical statistics at the level of a graduate textbook such as "Statistical Inference" by Casella and Berger, used by Stats 510/511. The comprehensive exam is offered twice a year, in late August and in late May. Students with advanced preparation may take this exam at the start of their first year. Two attempts are allowed, and the attempt at the start of the first year does not count towards this maximum of two. All students need to pass this exam within 12 months of enrolling in the program unless an exception is approved by the PhD Program Director.
- Applied statistics exam. This exam tests modeling and data analysis skills and is roughly based on Stats 600/601. It is given as a 3-day take-home exam once a year in late May. Two attempts are allowed. All students need to pass this exam within two years of enrolling in the program unless an exception is approved by the PhD Program Director.

### Program Requirements prior to Fall 2020

The Ph.D. in Statistics is flexible and allows students to pursue a variety of directions, ranging from statistical methodology and interdisciplinary research to theoretical statistics and probability theory. Students typically start the Ph.D. program by taking courses and gradually transition to research that will ultimately lead to their dissertation, the most important component of the Ph.D. program. The major requirements of the Ph.D. program are coursework, qualifying exams, advancement to candidacy, and dissertation.

### Required Courses

The core PhD curriculum consists of four course sequences, offered annually:

**Applied Statistics**— STATS 600 and 601**Theoretical Statistics**— STATS 610 and 611**Probability**— STATS 620 and 621**Computational Methods for Statistics**— STATS 507 and STATS 606 (*prior to Fall 2019: STATS 607 I and II, 608 I and II*)

Stats 600, 601, 610, 611, 620, and 621 are semester-long courses, and Stats 607 I and II, 608 I and II are half-semester modules. Any combination of two half-semester modules in the 607/608 sequence is equivalent to one course. All doctoral students must take at least 6 out of 8 required courses, with at least one course selected from each of the four sequences. A B+ average or higher in the six selected courses is required.

In addition, all students are required to complete two professional development seminar courses:

**STATS 810**, which covers research ethics and introduction to research tools. Must be taken in the first semester in the program.**STATS 811**, which focuses on technical writing and presentation skills. Students are strongly advised to complete this course as soon as they have a writing project on which to work, such as a prelim proposal or a manuscript draft. Most students take this course in their second or third year. This course is required for graduation but not for advancing to candidacy.

### First Year Course Placement

Our Ph.D. program admits students with diverse academic backgrounds. All PhD students take Stats 600/601 (the PhD level applied statistics sequence) in their first year. Students with less mathematical backgrounds typically take Stats 510/511 (the Master’s level probability and theoretical statistics) in the first year and PhD-level theory courses (610/611, 620/621) in their second year. Students who wish to take 600-level theory courses in their first year should take the Theory QR exam offered just before the fall semester of their first year. Based on the results, they will either be approved to go on to the 600-level courses, or advised to take Stats 510/511. Passing the theory QR exam automatically places a student in 600-level courses, but one may also score high enough to place in 600-level courses without clearing the theory QR. In all cases, the PhD Program Director will help students choose their individual path through the required courses.

### Qualifying Requirements

These requirements apply to students admitted in Fall 2019 and later. Students admitted in Fall 2018 can choose between the old requirements and the new requirements.

All doctoral students need to satisfy the Applied and Theoretical Statistics qualifying requirements (QR).

**Applied statistics QR**. This requirement is satisfied by passing a modeling and data analysis exam, roughly based on Stats 600/601. It is given as a 3-day take-home exam once a year in May. Two attempts are allowed. All students need to pass this exam within two years of enrolling in the program unless an exception is approved by the PhD Program Director.**Theoretical statistics QR**. This requirement may be satisfied by either excellent performance in certain courses (described below) or by passing the statistical theory exam offered once a year in late August. The exam covers probability and theoretical statistics at the level of a graduate textbook such as "Statistical Inference" by Casella and Berger, used by Stats 510/511. All PhD students need to satisfy the theoretical statistics QR by the beginning of their second year in the program unless an exception is approved by the PhD Program Director. A well-prepared student can opt to take this exam just before the start of their first year; if they do not pass, this attempt does not count. Whether they attempt this exam before the first year or not, all students can either qualify for an exemption based on course grades (see below) at the end of their first year, or take the exam in August just before the start of their second year. No further attempts are allowed.

A student can be exempt from taking the theoretical statistics QR exam based on coursework. To qualify for an exemption, the student can use their grades from two courses taken in their first year. One of the courses must be either Stats 510, 620, or 621 and the other course must be either Stats 511, 610, or 611. To qualify for an exemption, the average grade from the two chosen courses must be at least 3.65, and if at least one 500-level course is used, then the average must be at least 3.85. This is based on the conversion of letter grades to GPA points as follows: B- = 2.7, B = 3.0, B+ = 3.3, A- = 3.7, A = 4.0, A+ = 4.0.

Here are some examples of courses and grades that would qualify for an exemption:

- STATS 510 (A) and 511 (A-)
- STATS 510 (A) and 611 (A-)
- STATS 621 (A-) and 610 (A-)
- STATS 621 (B+) and 610 (A)

### Advancing to Candidacy

Students who have passed the qualifying exams are expected to find a faculty advisor and start research leading to their dissertation proposal. The PhD Program Director and the faculty mentor assigned to each first year student can assist with finding a faculty advisor. Students are expected to submit a dissertation proposal and advance to candidacy within three semesters from passing the qualifying exams. Requirements for advancing to candidacy are:

**At least 18 credit hours of graduate course work**, including at least 6 out of the required 8 core courses and Stats 810. A B+ average in the selected 6 core courses is required. Stats 808/809/818/819 (Department Seminar), Stats 990 (Dissertation Research) and similar non-graded courses do not count towards the credit requirement.**At least 4 credit hours of cognates**, which are 400- and higher-level courses from outside the Statistics department. All cognate course selections must be approved by the PhD Program Director.**Writing a dissertation proposal and passing the oral preliminary exam**which consists of presenting the proposal to the student's preliminary thesis committee.

A dissertation proposal should identify an interesting research problem, provide motivation for studying it, review the relevant literature, propose an approach for solving the problem, and present at least some preliminary results. The written proposal must be submitted to the preliminary thesis committee and the graduate coordinator ahead of time (one week minimum, two weeks recommended) and then presented in the oral preliminary exam. The preliminary thesis committee is chaired by the faculty advisor and must include at least two more faculty members, at least one of them from Statistics. The faculty on the preliminary thesis committee typically continue to serve on the doctoral thesis committee, but changes are allowed. Please see Rackham rules on thesis committees for more information.

At the oral preliminary exam, the committee will ask questions about the proposal and the relevant background and either elect to accept the proposal as both substantial and feasible, or ask for specific revisions, or decline the proposal. The unanimous approval of the proposal by the committee is necessary for the student to advance to candidacy.

### Additional Course Requirements

Students must take at least three additional PhD level semester-long courses or equivalent in half-semester modules. This requirement can be fulfilled with additional courses from the core sequences, advanced PhD courses, or topics courses. Stats 810, 811, and 750 (independent reading) do not count towards this requirement. While these additional courses are not required for advancement to candidacy, it is expected that students take at least some of them before advancing to candidacy. Taking courses after advancement to candidacy may require careful planning as candidates are allowed to take only one course per semester without an increase in tuition.

In addition, all PhD students are expected to register for Stats 808/809/818/819 (Department Seminar) every semester and attend the seminar regularly. Candidates registered for another course do not have to register for the department seminar, but are still expected to attend.

Exceptions to the above requirements may be granted by the PhD Program Director .

### Annual Progress Reports

Each candidate is required to meet with the members of their thesis committee annually. This could be in the form of either giving a short presentation on their research progress to the thesis committee as a group, or meeting with committee members individually.

Each committee member should complete a Thesis Committee Member Report and return it to the student. The student should share the completed Thesis Committee Member Reports with both the PhD Program Coordinator and their advisor.

All meetings with the committee members should take place by **April 15.**

Following the meetings, the student and the advisor should complete the Annual PhD Candidate Self-Evaluation and Feedback Form. The advisor should review the committee members’ Thesis Committee Member Reports and take them into account when completing the advisor’s portion. The completed Annual PhD Candidate Self-Evaluation and Advisor Feedback Form must be submitted to the PhD Program Coordinator by **May 31. **The completed form will be saved with the department, and a copy will be shared with the student.

### Dissertation and Defense

Each doctoral student is expected to write a dissertation that makes a substantial and original contribution to statistics or a closely related field. This is the most important element of the doctoral program. After advancing to candidacy, students are expected to focus on their thesis research under the supervision of the thesis advisor and the doctoral committee. The composition of the doctoral committee must follow the Rackham's guidelines for dissertation committee service. The written dissertation is submitted to the committee for evaluation and presented in an oral defense open to the public.

### Rackham Requirements

The Rackham Graduate School imposes some additional requirements concerning residency, fees, and time limits. Students are expected to know and comply with these requirements.