Graduate Program: Doctoral Degree

Our doctoral program in Statistics and Applied Probability prepares graduate students to expand the boundaries of statistical theory and practice. Graduates are trained for a career in academics or industry where they are at the forefront of new methods and technology. Our students are given rigorous mathematical training in statistics and probability that can be used to develop real-world methodologies. Recent dissertations have been written in the areas of smoothing splines, spatial statistics, micro-array analysis, functional data models, empirical processes, mathematical and statistical finance, Bayesian inference, and bootstrap estimation methods.

The department offers an optional emphasis in Financial Mathematics and Statistics (FMS). The FMS emphasis allows students to specialize in the emerging field of financial mathematics and statistics. The Center for Research in Financial Mathematics and Statistics provides students a great opportunity to work with a thriving group of researchers taking a cross-disciplinary approach to financial mathematics.

In addition, the department participates in the Quantitative Methods in the Social Sciences (QMSS) interdisciplinary PhD emphasis. The QMSS emphasis offers students an opportunity to apply cuting-edge statistical techniques to research in anthropology, communications, education, geography, political science, psychology, or sociology.

Degree Requirements for PhD in Statistics & Applied Probability

Course Requirements:
Students must complete 72 units of PSTAT graduate courses or approved graduate courses from other departments and pass two qualifying exams. At least 60 of the 72 required units must be in Pstat 200 level graduate courses (excluding P/Stat 263), and they must include PSTAT 207 A-B-C, 213 A-B-C and 220 A-B-C. Each required course must be completed with a grade of B or better.

Qualifying Exams (Part of the area requirement):
Each student must pass two qualifying exams at the PhD level. Each student may attempt each qualifying exam twice. Each student must successfully pass two area exams within three years after joining the Department’s Graduate program regardless of having a Master’s degree or not.

There are four qualifying exam options:

Mathematical Statistics
Probability and Stochastic Processes
Applied Statistics
Pure Mathematics (administered by the Mathematics Department)

For more detailed explanations regardingthe Area Requirements and Qualifying Exams, please see our Department Policies and Procedures.

Committee Nomination and Advancement to Candidacy:
The nomination of the dissertation committee is a process that happens before the advancement to candidacy and requires separate paperwork and approval. Eligibility of service on dissertation committees is governed by Academic Senate Regulations and the Graduate Council. The rules are as follows;

Committee must consist of a minimum of 3 UC ladder faculty
Two, including the Chair, must be in home department
Additional members are at the department’s digression
If the student wants to nominate a non-ladder faculty member (such as a non SOE or PSOE lecturer, researcher, adjunct faculty, or visiting faculty) as the second or third member of their committee, an exception request must be made using the PhD Form I or I-A. Consult the Graduate Handbook or the Graduate Program Assistant for further instructions.

A student is eligible to advance to candidacy after the required courses are completed and the qualifying exams are passed. Students are expected to nominate their dissertation committee and advance to doctoral candidacy after 2-3 years of joining the department, but no later than the end of the third year. PhD students must pass the oral examination given by the committee before advancing to candidacy. This oral includes a satisfactory presentation of the proposed research topic and the results of preliminary reading and research.

Dissertation Requirements:
Students complete the requirements for the Ph.D. with the oral dissertation defense to the Doctoral Committee, and by filing their dissertation with the Graduate Division. The candidate for the Ph.D. must make his/her dissertation available to all the members of the Ph.D. committee at least two weeks in advance of the date of the defense. An electronic copy must also be made available to the Graduate Program Assistant for possible examination by other members of the faculty and/or graduate students. Students must inform the Graduate Program Assistant that they will be defending their dissertation at least one month prior to the date of the defense. The dissertation defense is public, and will be announced to the department via email. For information on dissertation filing or formatting, please consult the Graduate Division’s Academic Section.

Other Resources:

PhD Requirements Sheet

Detailed instructions for nominating your committee and advancing to candidacy

Optional PhD Emphasis in Financial Mathematics and Statistics

Students pursuing a Ph.D. may petition to add an emphasis in financial mathematics and statistics. (This emphasis formalizes the study of and research in financial mathematics, which is a major growth area within the fields of applied probability and statistics.) Students are required to accumulate 72 graduate units, of which 44 are in required courses.

Required Courses:
PSTAT 207 A-B-C
PSTAT 213 A-B-C
PSTAT 223 A-B-C
MATH 201 A-B

Electives:
PSTAT 220 A-B-C
PSTAT 221 A-B-C
PSTAT 222 A-B-C
PSTAT 262FM
ECON 210 A-B-C
ECON 235 A-B (Money and Finance)
PSTAT 274 or ECON 245 B (Econometric Theory Time Series)
MATH 201 C(Topics in Real Analysis)
MATH 206 A-B-C-D (Numerical Methods)
MATH 228 A-B-C (Functional Analysis)
MATH 246 A-B-C (PDEs)
With prior approval from the coordinating committee for the emphasis, other courses can be chosen as electives.

Qualifying Examinations:
1. Mathematical Statistics (based on the required course sequence PSTAT 207 A-B-C)
2. Probability and Stochastic Processes (based on the required course sequence PSTAT 213 A-B-C)

Committee must consist of a minimum of 3 UC ladder faculty
Two, including the Chair, must be in home department
Additional members are at the department’s digression
If the student wants to nominate a non-ladder faculty member (such as a non SOE or PSOE lecturer, researcher, adjunct faculty, or visiting faculty) as the second or third member of their committee, an exception request must be made using the PhD Form I or I-A. Consult the Graduate Handbook or the Graduate Program Assistant for further instructions.

A student is eligible to advance to candidacy after the required courses are completed and the qualifying exams are passed. Students are expected to nominate their dissertation committee and advance to doctoral candidacy after 2-3 years of joining the department, but no later than 4 years. PhD students must pass the oral examination given by the committee before advancing to candidacy. This oral includes a satisfactory presentation of the proposed research topic and the results of preliminary reading and research.

Dissertation Requirements:
The student's doctoral committee shall be appointed according to the same regulations governing other Ph.D. students in Statistics and Applied Probability and must be approved by the coordinating committee for the emphasis. The topics of dissertations must focus on an area within financial mathematics and statistics and be approved by the student's doctoral committee.

Other Resources:

FMS Requirements Sheet

FMS Website

Optional PhD Emphasis in Quantitative Methods in the Social Sciences

The QMSS curriculum is designed to provide students with the rigorous mathematical and statistical background necessary for advanced quantitative work. Required Courses:
		• Math 3A and 3B (Calculus with Applications) • Math 108A (Introduction to Linear Algebra) • A one year sequence of statistics (for instance, Psychology 221A, B, and C, or the equivalent year-long sequence offered in many participating departments).
These requirements can be met with equivalent courses, or waived if equivalent courses have already been completed.
The QMSS curriculum is also designed to provide a broad interdisciplinary perspective on the use of quantitative methods in the social sciences. To meet that requirement we require:
		• At least three quantitative social science methods courses, at least two of which are outside the student's home department. A list of courses that satisfy this requirement is here. • Enrollment in the QMSS colloquia for at least three quarters. • At least one presentation of original quantitative social science research at the QMSS colloquia.
Dissertation Requirements The QMSS curriculum is designed to train students to conduct quantitative social science research that draws on or has implications for the social sciences beyond the student's Ph.D. discipline. To that end we require:
		• A Ph.D. dissertation that is focused on an issue that is appropriate to the QMSS emphasis. For instance, the dissertation could develop a quantitative method that could be applied to social science fields beyond the student's discipline, or adapt a quantitative method used in a social science field outside the student's discipline for researching a substantive problem within the student's discipline. • A dissertation committee that includes at least one core QMSS faculty member from outside the student's home department. Note that according to the most recent Academic Senate requirements, the committee must include at least three UC ladder faculty members, two of whom must be members of the home department. One of the home department members must serve as chair or co-chair.
Upon Completing These Requirements Once completing the requirements listed above, students should submit all records of courses, seminars, and research to the QMSS Coordinating Committee, which will certify to the Graduate Division that the requirements for the emphasis have been satisfied. The Graduate Division will verify completion of the emphasis and convey this information to the Registrar, which will in turn include the QMSS emphasis on the final transcript. Students who complete the requirements will graduate from their home department with an emphasis in QMSS — for example, a student in the Education department who completes the requirements will receive a Ph.D. in "Education, with an emphasis in Quantitative Methods in the Social Sciences."

The student's doctoral committee shall be appointed according to the same regulations governing other Ph.D. students in Statistics and Applied Probability and must be approved by the coordinating committee for the emphasis. The topics of dissertations must focus on an area within financial mathematics and statistics and be approved by the student's doctoral committee.

PSTAT 262 FM is a seminar course reserved for topics in financial mathematics and statistics.

Other Resources:

QMSS Homepage

Directions on how to join QMSS

Participating Departments