III. THE PH.D. PROGRAM:

The Department of Statistics and Probability at Michigan State University has had an established Ph.D. program since 1955, one of the oldest in the country. Either statistics or probability can be emphasized.

The Department would like to attract into its Ph.D. program those students who have ability in and enjoy mathematics and its applications. We believe that students with solid training and interest in mathematics will be able to make a contribution to the field of statistics and probability, and we particularly welcome applications from undergraduate and graduate mathematics majors who have studied some probability or statistics.

A student without previous graduate work is usually admitted to the M.S. program, even if planning to work toward the Ph.D. Graduate courses taken while a M.S. student counts toward satisfaction of the Ph.D. requirements. A student with previous graduate work may be admitted directly to the Ph.D. program. Each student is assigned an advisor who helps plan the student's program, taking into account the student's goals and the courses and seminars appropriate to these goals.

III.1 The Guidance Committee

Every student will have a Guidance Committee as soon as he/she enters the Ph.D. program. An advisor selected by the department will chair it and it will have 3 more members: the current instructor for STT 871, the current instructor for STT 881 and the Graduate Director. The committee must approve the course selection of the student.

The Guidance Committee will be reconstituted as soon as the student selects a thesis advisor. This normally will occur during the second year. It will consist of at least three faculty members of this Department and at least one from outside the Department as determined by the thesis advisor in consultation with the student. The primary responsibility of the committee will be to advise the student in his/her thesis research.

III.2 Course Work

STT 871-2, STT 881-2, STT 863 are the core courses, with 10 additional courses as follows:

1. At least 5 courses from among (a) and (b):
(a) Advanced Probability: STT 961, 964, 996 (at least 2)
(b) Advanced Statistics: STT 953, 954, 997 (at least 2)

2. At least 5 electives: Graduate courses taken inside or outside the Department.

NOTE: STT 996 and STT 997 are special topic courses, which may change from year to year. For descriptions of the courses see Pages 22 - 31 or www.reg.msu.edu/courses/request.asp.

A working knowledge of real analysis is required for successful completion of the Ph.D. program. Students without sufficient background must take Real Analysis I, (MTH 828) prior to (or concurrent with) STT 871 or STT 881. MTH 828 can be counted as an elective. A student entering with rigorous real analysis and 861-2 level probability and statistics might take a program approximating the following: (Such students should review their previous work in real analysis. A placement examination may be used to confirm readiness.)

STT 953, 954, 997 and STT 961, 964, 996 are offered as follows:
953 Asymptotic Theory (Fall, even years)
954 Semi-Nonparametric Inference (Fall, odd years)
997 Advanced Topics in Statistics (Fall, Spring, Summer)
961 Convergence of Measures and Stochastic Processes(Fall, odd years)
964 Stochastic Analysis (Spring, even years)
996 Advanced Topics in Probability (Fall, Spring, Summer)

Year 1 Ph.D. Program

NOTE: STT 881-2 is a rigorous sequence in measure theory and probability. STT 871-2 is a rigorous sequence in mathematical statistics. STT 863 is a course on applied statistical methods. STT 864 is a course on more advanced applied statistical methods. STT 865 is a course on modern statistical methods. STT 864 and 865 are offered in alternating spring semesters

Ph.D. Program (Year 2)

During Fall and Spring of the second year, the student will need to take a 900 level probability and a 900 level statistics class each semester. The third course each semester is an elective.

At this point in the Ph.D. program (after Spring semester of the second year) a student will have completed the core courses, the 900 level STT courses and 3 electives on applications. The other courses could be taken in the Summer and in the third year of study. A student's program is always subject to the approval of the Guidance Committee.

Summer offerings

The offerings of the Department in the summers are light. Students usually use the time to prepare for examinations or for thesis research. One or two graduate courses are offered each summer with topics varying, almost always 996 or 997. In the past few summers, graduate courses were offered in non-parametric density estimation, Bayesian statistics, analysis of contingency tables, chaos theory, stochastic models in biology, finance, inference for stationary processes, reliability and survival analysis, limit theorems for dependent random variables, density estimation, curve estimation and wavelets, statistical inference for Markov and general stochastic processes, graphical methods in regression, and, statistical inference for images.

III.3 Examinations

Two written examinations (on probability at the level of STT 881- 882, and on statistics at the level of STT 871-872) are required of all Ph.D. candidates. The exams will be given twice a year near the beginning of Fall semester and Spring semesters. In order to remain in the doctoral program, a student is required to pass the preliminary examinations on probability and statistics by the Spring semester following his or her enrollment in STT 882 and STT 872. To continue in the Ph.D. program, a student must pass these two exams in at most two attempts for each.

III.4 Attendance at Colloquia and Seminars

The Department has colloquia which meet regularly on Tuesdays at 10:20-11:10 a.m. Speakers are either members of the Department or are statisticians, probabilists, or those conducting research in other disciplines. The Department strongly recommends attendance by doctoral students, and occasionally, by masters students. In addition, seminars on statistics or probability are regularly scheduled in which both professors and doctoral students participate.

III.5 Thesis

A doctoral candidate must demonstrate the ability to carry out significant original research in statistics and probability. This is accomplished through the writing of a dissertation under the direction of a thesis advisor. It is the responsibility of the student to find a thesis advisor. Copies of theses written by former students are available in the Department’s Katz Library. The candidate defends his/her thesis in an oral examination attended by the Guidance Committee. The candidate must present the results of his/her thesis research in a talk of approximately one hour is open to the public. After that presentation, the Guidance Committee meets further in a closed session to determine whether the student’s thesis should be approved. The thesis must be submitted in a form acceptable to the Graduate School. Deadline dates are available from the Graduate School (355-0300 or http://www.msu.edu/user/gradschl/). A bound copy of the thesis must be submitted to the Department. The thesis is microfilmed by the university. There is a charge for this service .

III.6 Annual Progress Report for Ph.D. Students

In May or June of each year the student must submit an "Annual Progress Report for Ph.D. Students." This form is available from http://grad.msu.edu/progress.htm. See the Appendix. The chairperson of the student's Guidance Committee is responsible for completion of the second page of the report. Students who hold assistantships and international students on F-1 visas are expected to complete nine credits which contribute to the completion of the degree each of Fall and Spring semesters. Those holding assistantships during the summer must complete at least three such credits. Students who have completed or have begun thesis research may carry fewer numbers of credits, keeping in mind the university requirement that a Ph.D. candidate must complete 24 credits of 999 courses (thesis research).