A total of 72 graduate units are required, consisting of the following:

• 18 required coursework units in fundamental topics and exam fields
• 18 elective coursework units
• Two qualifying exams in statistics
• Teaching Requirement for PhD Students from the Office of Graduate Studies, Arts & Sciences
• Oral presentation
• Dissertation research, thesis preparation, and defense (up to 36 optional coursework units)

General requirements: Completion of the PhD requires at least four full years of graduate study (72 units), with at least 48 units completed in residence at Washington University. The student must spend at least one academic year as a full-time student; this requirement cannot be met wholly by summer sessions or part-time study. The student may, with departmental permission, transfer a maximum of 24 graduate credits from other universities. The typical course load is 9 credit units per semester. A GPA of B (3.0) or better is required in graduate course work.

Graduate students in statistics may ordinarily expect up to five years of support. Continuation of support each year is dependent upon normal progress toward the degree and the satisfactory performance of duties. Teaching experience is an increasingly important component of graduate education for students who seek academic employment. The PhD in statistics program provides the opportunity for students to work as Assistants to the Instructor and to learn how to teach technical topics to students with a wide range of backgrounds.

For the well-prepared student, "normal progress" usually means the following:

• At the end of the second year, the student has successfully passed the two statistical qualifying exams associated with SDS 5061 Theory of Statistics I–SDS 5062 Theory of Statistics II and SDS 5071 Advanced Linear Models I–SDS 5072 Advanced Linear Models II . They have also completed the courses SDS 5310 Bayesian Statistics and SDS 5210 Statistical Computation.
• At the end of the third year, the student has completed the candidacy requirement.
• At the end of the fourth year, the student has completed the 72-unit course requirement and is making substantial progress on a thesis.

Students must also complete the Teaching Seminar course (Math 597), which prepares them for both Assistant to the Instructor work and academic teaching duties, which are integral to all scholarly activities. For a typical PhD student, the course is taken twice: once in the spring of the first year and again in the fall of the second year. Each student will have departmental duties (e.g., grading, proctoring) of no more than 15 hours per week as Assistant to the Instructor. Students must also complete a Professional Development course (Math 598).

Please note that the sequence outlined above is for "well-prepared" students. The exact point at which any student enters the sequence depends on their ability and background. When warranted, deviation from the normal sequence is permissible, and a tailored program that fits the student's ability and background will be followed.

Specific course requirements: The 72 units of course work must include two basic graduate-level sequences in statistics: SDS 5061 Theory of Statistics I–SDS 5062 Theory of Statistics II and SDS 5071 Advanced Linear Models I–SDS 5072 Advanced Linear Models II; the following statistics courses: SDS 5310 Bayesian Statistics and SDS 5210 Statistical Computation. In exceptional circumstances, departmental permission may be requested to replace one of these sequences with a suitable alternative. The student may also petition the department to waive one or more of these sequences because of work completed previously.

Prerequisites, if needed, are advanced undergraduate courses in linear algebra and real analysis. Such courses would count as 0 credits toward the PhD degree.

It is in each student's best interest to take the two sequences that contain the material covered in the qualifying exams as soon as their individual program allows. Sequels to these courses, at the 500 level, are frequently offered. The qualifying exam courses are generally prerequisites to these 500-level courses.

Prior to finding a research advisor, students are welcome to take any of the Department of Statistics and Data Science 500-level statistics electives, and they may also take reading courses with statistics faculty members (SDS 500/Math 590 Research). Statistics electives offered by the department include the following:

Course List

Code	Title	Units
SDS 5070	Stochastic Processes	3
SDS 5120	Survival Analysis	3
SDS 5155	Time Series Analysis	3
SDS 5210	Statistical Computation	3
SDS 5310	Bayesian Statistics	3
SDS 5430	Multivariate Statistical Analysis	3
SDS 5440	Mathematical Foundations of Big Data	3
SDS 5480	Topics in Statistics	3
SDS 5531	Advanced Statistical Computing I	3
SDS 5532	Advanced Statistical Computing II	3
SDS 5595	Topics in Statistics: Spatial Statistics	3
SDS 579	Topics in Statistics	3

Prior to finding a research advisor, students may submit a request to the graduate committee to take a course outside of the department. A decision on such requests will be made in consultation with statistics faculty members.

Students are encouraged to take reading courses with department faculty to learn about the research interests of potential advisors. After the student has found a research advisor and a research topic, the advisor may suggest that the student take some additional courses from other departments that may be useful for the student's research program.

Elective courses taken in other departments allow students to supplement their statistics coursework with other topics that may be helpful for their research and professional development. Some popular elective courses offered by other departments include the following:

Course List

Code	Title	Units
CSE 511A	Introduction to Artificial Intelligence	3
CSE 514A	Data Mining	3
CSE 517A	Machine Learning	3
CSE 519T	Advanced Machine Learning	3
CSE 541T	Advanced Algorithms	3
Econ 5145	Advanced Theoretical Econometrics	3
ESE 405	Reliability and Quality Control	3
ESE 407	Analysis and Simulation of Discrete Event Systems	3
ESE 415	Optimization	3
ESE 425	Random Processes and Kalman Filtering	3
ESE 428	Probability	3
ESE 520	Probability and Stochastic Processes	3
ESE 521	Random Variables and Stochastic Processes I	3
ESE 522	Random Variables and Stochastic Processes II	3
ESE 523	Information Theory	3
PHS 550	Randomized Controlled Trials	3
Math 5160	Complex Variables	3
Math 5051	Measure Theory and Functional Analysis I	3
Math 5052	Measure Theory and Functional Analysis II	3
Math 5501	Numerical Applied Mathematics	3
Math 5560	Topics in Financial Mathematics	3
MSB 623	Advanced Topics in Biostatistics	3

Language requirement: All students must demonstrate proficiency in English.

If English is not the student's native language, they must pass an oral English proficiency exam with a grade of 3 or better. If the student does not score a 3 the first time they take the exam, the director of English Language Programs for Arts & Sciences will recommend that the student take one or more classes to improve reading, writing, pronunciation, listening, or speaking skills. After the recommended classes have been completed, the student is required to retake the English proficiency exam. Once the student has demonstrated the ability to handle teaching a class (by scoring a 3 or better on the exam), they will qualify for Assistant to the Instructor or Course Instructor duties.

Qualifying examinations and candidacy requirements: The qualifying exam and candidacy requirements constitute two separate requirements. The qualifying exam is a series of two written tests that cover a range of topics; the candidacy requirement is an oral presentation and thesis proposal.

The written tests cover the material in the two basic statistics course sequences, SDS 5061 Theory of Statistics I–SDS 5062 Theory of Statistics II and SDS 5071 Advanced Linear Models I–SDS 5072 Advanced Linear Models II. Each spring, at the end of the SDS 5061 Theory of Statistics I–SDS 5062 Theory of Statistics II and SDS 5071 Advanced Linear Models I–SDS 5072 Advanced Linear Models II sequences, all students enrolled in these courses take a two-hour final exam; this exam usually covers the second half of the sequence. Doctoral candidates take an additional one-hour exam that covers the entire sequence. To pass the qualifying exam, the student must pass the three-hour combined exam.

Because each sequence varies somewhat in content from year to year, it is recommended that the student take each set of exams at the conclusion of the sequence in which they are enrolled. No advantage is gained by delaying the exam for a year. It is desirable to make every effort to finish all three exams by the end of the second year of study.

Some students will enter the PhD program with previously acquired expertise in one or more of the three basic sequences. This situation sometimes happens with students who transfer from other PhD programs or who come from certain foreign countries. Such students may formally petition the chair of the graduate committee to be exempted from the appropriate course and its qualifying exam. The petition must be accompanied by hard evidence (e.g., published research, written testimony from experts, records of equivalent courses, examinations and the grades achieved on them). The graduate committee will make the final judgment on all exemption requests.

Once the written phase of the qualifying process is complete, the student is ready to begin specialized study. By the third year of study, the student must complete the candidacy requirement. The student must form a preliminary thesis committee called a Research Advisory Committee that includes their advisor and at least two other faculty members. In discussion with the advisor and the preliminary thesis committee, the student will select a topic and a body of literature related to this topic. The student will prepare a one-hour oral presentation related to the topic and a two-page thesis proposal that demonstrates mastery of the selected topic. The oral presentation is designed to expedite specialized study and to provide guidance toward the thesis. The preparatory work for the thesis proposal often becomes the foundation on which the thesis is constructed.

After the student completes the oral presentation, work on the thesis begins.

The dissertation and thesis defense: The student's dissertation is the single most important requirement for the PhD degree; it must be an original contribution to the knowledge of statistics, probability, and/or applied probability and is the student's opportunity to conduct significant independent research.

It is the student's responsibility to find a thesis advisor who is willing to guide their research. Since the advisor should be part of the oral presentation committee, the student should have engaged an advisor by the beginning of the third year of study.

Once the department has accepted the dissertation (on the recommendation of the thesis advisor), the student is required to defend their thesis through a presentation accompanied by a question-and-answer period.

For information about preparing the thesis and its abstract as well as the deadlines involved, including the creation of the Research Advisory Committee and the Dissertation Defense Committee, please consult the Office of Graduate Studies, Arts & Sciences. Please use these additional relevant resources: the Doctoral Dissertation Guide, the Forms page, and the Policies and Procedures page.