;

# Statistical Science Ph.D.

## Introduction

Students in the statistical science program learn to develop and use statistical methods to provide a probabilistic assessment of the variability in different data structures. This knowledge is applied to the quantification of the uncertainties inherent in the discoveries, summaries and conclusions that are drawn from the data analysis. The Ph.D. program provides mastery of fundamental concepts in statistical theory and methods, as well as analytical and computational skills to build modern statistical models, implement them, and effectively communicate their results. Through the process of learning these skills, the students develop the ability to conduct independent research.

Students will obtain a Ph.D. in statistical science. More specifically, students will develop background on statistical theory, methods, and computing through the program coursework, with research emphasis on novel methods and applications.

We will accept students with undergraduate degrees in fields that include computer science, engineering, mathematics, natural sciences, physics, and statistics, subject to appropriate course requirements in statistics and mathematics. Undergraduate preparation in mathematics and statistics should include: single variable and multivariate differential and integral calculus (UC Santa Cruz equivalent AM 11A, AM 11B or MATH 19A, MATH 19B, and MATH 23A, MATH 23B); linear algebra (UCSC equivalent AM 10 or MATH 21); introductory statistics (UCSC equivalent STAT 5 or STAT 7); and introductory calculus-based probability and statistical inference (UCSC equivalent STAT 131 and STAT 132).

### Relationship of M.S. and Ph.D. programs

The M.S. and Ph.D. programs are freestanding and independent, so that students can be admitted to either. Students completing the M.S. program may proceed into the Ph.D. program upon successful completion of the pre-qualifying examination, and application to the graduate committee and acceptance. Students in the Ph.D. program have the option of receiving the M.S. degree upon completion of the M.S. program requirements, including the capstone research project. Ph.D. core courses STAT 205B and STAT 206B can be used in place of STAT 205 and STAT 206, respectively, to fulfill the M.S. degree course requirements.

### Course Requirements

#### Nine core courses

Ph.D. students must complete nine core courses: seven 5-credit courses listed below; a 3-credit course on research and teaching (STAT 200); and a 2-credit research seminar (STAT 280B). Ph.D. students must complete four additional 5-credit courses from the approved list of elective courses, bringing the total non-seminar credit requirements to 58 credits. None of the additional elective courses required to satisfy the credit requirements for the Ph.D. program can be substituted by independent study courses (Independent Study/Research or Thesis Research).

Students in the Ph.D. program must take the following nine core courses:

 STAT200 Research and Teaching in Statistics 3 STAT203 Introduction to Probability Theory 5 STAT204 Introduction to Statistical Data Analysis 5 STAT205B Intermediate Classical Inference 5 STAT206B Intermediate Bayesian Inference 5 STAT207 Intermediate Bayesian Statistical Modeling 5 STAT208 Linear Statistical Models 5 STAT209 Generalized Linear Models 5 STAT280B Seminars in Statistics 2

#### 5-credit core courses

All core courses are 5-credit courses, except for STAT 200 and STAT 280B. STAT 200 is a 3-credit course which covers basic teaching techniques for teaching assistants, and examines research and professional training items, as well as ethical issues relating to research in science and engineering. STAT 280B is a 2-credit seminar course, which involves attending the Statistics Department colloquia and participating in the discussion session after the seminar presentation. The strict requirement for STAT 280B is for students to take it once in their first year in the program. However, students are strongly recommended to take STAT 280B each quarter throughout their graduate studies.

All core courses must be taken for a letter grade (except for STAT 200 and STAT 280B, which are given on a satisfactory/unsatisfactory basis). In order to maintain a full load for graduate standing after their first year, students take additional courses, including independent study courses, from the approved list of elective courses, appropriate to their research interests and selected in consultation with their advisers.

Electives available to PhD students include:

 STAT202 Linear Models in SAS 5 STAT209 Generalized Linear Models 5 STAT222 Bayesian Nonparametric Methods 5 STAT223 Time Series Analysis 5 STAT224 Bayesian Survival Analysis and Clinical Design 5 STAT225 Multivariate Statistical Methods 5 STAT226 Spatial Statistics 5 STAT229 Advanced Bayesian Computation 5 STAT243 Stochastic Processes 5 STAT244 Bayesian Decision Theory 5 STAT246 Probability Theory with Markov Chains 5 AM216 Stochastic Differential Equations 5 AM230 Numerical Optimization 5 AM250 An Introduction to High Performance Computing 5 CSE242 Machine Learning 5 CSE243 Data Mining 5 CSE249 Large-Scale Web Analytics and Machine Learning 5 CSE272 Information Retrieval 5 CSE277 Random Process Models in Engineering 5 ECE253 Introduction to Information Theory 5 ECE256 Statistical Signal Processing 5 ECON211A Advanced Econometrics I 5 ECON211B Advanced Econometrics II 5 ENVS215A Geographic Information Systems and Environmental Applications 5 ENVS215L Exercises in Geographic Information Systems 2 MATH204 Analysis I 5 MATH205 Analysis II 5 MATH208 Manifolds I 5

ENVS 215L is the concurrent lab to ENVS 215A. The lecture/lab combination counts as one course.

### Teaching Requirements

Ph.D. students are required to serve as teaching assistants for at least one quarter during their graduate study. Certain exceptions may be permitted for those with extensive prior teaching experience, for those who are not allowed to be employed due to visa regulations, or for other reasons approved by the director of graduate studies.

### Pre-Qualifying Requirements

At the end of the first year, Ph.D. students take a pre-qualifying examination covering six 5-credit core courses: STAT 203, STAT 204, STAT 205B, STAT 206B, STAT 207 and STAT 208. This examination comprises two parts: an in-class written examination, followed by a take-home project involving data analysis. Students who do not pass this examination can retake it before the start of the following fall quarter; if they fail the second examination they are dismissed from the Ph.D. program, but have the option to continue in the M.S. program.

### Qualifying Examination

Ph.D. students must complete the qualifying examination (advancement to candidacy) requirement by the end of the spring quarter of their third year. Ph.D. students must select a research adviser by the end of their second year in the program. A written dissertation proposal must be submitted to the adviser, and filed with the Graduate Student Affairs Office. A qualifying examination committee will be formed, consisting of the adviser and at least three additional members, approved by the director of graduate studies and the dean of the Graduate Division. The following conditions must be met for the examination committee:

1. The chair of the qualifying examination committee must be a tenured faculty from within the graduate program faculty. The committee chair can not be the student’s adviser or one of her/his co-advisers.
2. For students with a single adviser, or two co-advisers one of which is from outside the graduate program faculty, the committee must include at least two members from within the graduate program faculty other than the adviser or co-adviser. For students with two co-advisers that are both members of the graduate program faculty, the committee must include at least one additional member from within the graduate program faculty.
3. The committee must include at least one member from outside the graduate program faculty, for which the Senate Regulations for committee membership apply. The outside member can be the student’s adviser or co-adviser.

The student submits the written dissertation proposal to all members of the committee no less than one month in advance of the qualifying examination. The dissertation proposal is formally presented in a public oral qualifying examination with the committee, followed by a private examination. Students will advance to candidacy after they have completed all course requirements (including removal of any incompletes), passed the qualifying examination, nominated a dissertation reading committee, and paid the advancement to candidacy fee. Under normal progress, a student will advance to candidacy by the end of the spring quarter of her/his third year. A student who has not advanced to candidacy by the start of the fourth year will be subject to academic probation.

## Dissertation

### Dissertation Defense

The completed dissertation must be submitted to the reading committee at least one month before the dissertation defense, which consists of a public presentation of the research followed by a private examination by the reading committee. Successful completion of the dissertation defense is the final requirement for the Ph.D. degree.

Students will be admitted to the Ph.D. program, not to the research group of any individual faculty member. However, each student will be matched with a first-year mentor, to ensure that adequate guidance is provided in the crucial first year of graduate school. In later years, the role of the mentor will be played by the Ph.D. dissertation adviser. Faculty advisers will be responsible for charting the progress of their students on a regular basis, and for making necessary adjustments to their plan of study and research.

The graduate program faculty will meet in the spring quarter of each academic year to review the performance of all students in the program. Based on the results from the faculty review, a written report will be provided to each student with an assessment of her/his performance and description of specific program objectives for the following academic year.

The normative pre-candidacy period for Ph.D. students (enrolled full-time) is three years and the normative candidacy period is two years, for a total of five years to the Ph.D. degree.

### Transfer Credit

Up to three School of Engineering courses fulfilling the degree requirements of the Ph.D. degree may be taken before beginning the graduate program through the concurrent enrollment program. Ph.D. students who have previously earned a M.S. degree in a related field at another institution may substitute courses from their previous university with approval of the adviser and the graduate committee. Petitions should be submitted along with the transcript from the other institution or UC Santa Cruz Extension. For courses taken at other institutions, copies of the syllabi, examinations, and other course work should accompany the petition. Such petitions are not considered until the completion of at least one quarter at UCSC. At most, a total of three courses may be transferred from concurrent enrollment and other institutions.