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Doctor of Philosophy in Statistics

The department looks for students who wish to prepare for research careers in statistics or probability, either applied or theoretical. Advanced undergraduate or master's level work in mathematics and statistics provides a good background for the doctoral program. Quantitatively oriented students with degrees in other scientific fields are also encouraged to apply for admission. In particular, the department is expanding its research and educational activities towards computational biology, mathematical finance and information science, via a VIGRE program. The program normally takes four years to complete.

Program Summary—STATS 300A,B,C, 305, 306A,B, and 310A,B,C (first-year core program); pass two of three parts of the qualifying examinations (end of first year); breadth requirement (second or third year); successfully complete the thesis proposal meeting (before end of third year); pass the University oral examination (fourth year); dissertation (fourth year).

In addition, students are required to take 9 units of advanced topics courses offered by the department (including at least two of the following: 314, 317, 318, 315A, or 315B, but not including literature, research, or consulting), and 3 units of 390 statistical consulting. All students who have passed the qualifying exams but have not yet passed the University oral examination must take 319 at least once per year.

First-Year Core Courses—STATS 300 systematically surveys the ideas of estimation and of hypothesis testing for parametric and nonparametric models involving small and large samples. 305 is concerned with linear regression and the analysis of variance. 306 surveys a large number of modeling techniques, related to but going beyond the linear models of 305. 310 is a measure-theoretic course in probability theory, beginning with basic concepts of the law of large numbers and martingale theory. Students who do not have enough mathematics background can take 310 after their first year but need to have their first-year program approved by the Ph.D. program adviser.

Qualifying Examinations—These are intended to test the student's level of knowledge when the first-year program, common to all students, has been completed. There are separate examinations in the three core subjects of statistical theory and methods, applied statistics, and probability theory, and all are typically taken during the summer between the student's first and second years. Students may take two or three of these examinations and are expected to show acceptable performance in two examinations.

Breadth Requirement—Students are advised to choose an area of concentration in a specific scientific field of statistical applications; this can be realized by taking at least 15 units of course work approved by the Ph.D. program adviser.

Current areas with suggested course options include:

Computational Biology and Statistical Genomics—Students are expected to take 9 units of graduate courses in genetics or neurosciences (imaging), such as GENE 203/BIO 203, as well as 9 units of classes in Statistical Genetics or Bioinformatics, GENE 344A,B, STATS 345, STATS 366, STATS 367.

Machine Learning—Courses can be chosen from the following list:

Statistical Learning: STATS 315A and 315B

Data Bases: CS 245, 346, 347

Probabilistic Methods in AI: CS 221, 354

Statistical Learning Theory and Pattern Classification: CS 229

Applied Probability—Students are expected to take 15 units of graduate courses in some of the following areas:

Control and Stochastic Calculus: MS&E 322, 351, MATH 237, EE 363

Finance: STATS 250, FINANCE 622, MATH 236

Information Theory: EE 376A, 376B

Monte Carlo: STATS 318, 345, 362, MS&E 323

Queuing Theory: GSB 661, 663, MS&E 335

Stochastic Processes: STATS 317, MATH 234

Earth Science Statistics—Students are expected to take:

STATS 317, 318, 352

and three courses from the GES or Geophysics departments, such as GES 144 or GEOPHYS 210.

Social and Behavioral Sciences—Students are expected to take three advanced courses from the department with an applied orientation such as:

STATS 261/262, 324, 343, 354

and three advanced quantitative courses from departments such as Anthropology, Economics, Political Science, Psychology, and Sociology, and the schools of Education, Business, or Medicine.

Ph.D. Thesis Meeting and University Oral Examinations—The thesis proposal meeting is intended to demonstrate students' depth in some areas of statistics, and to examine the general plan for their research. In the meeting, they will give a short presentation and discuss their ideas for completing a Ph.D. thesis, with a committee consisting of their advisor and thesis committee (a total of three members). The meeting must be successfully completed before the end of their third year. If the student does not pass, the exam must be repeated. Repeated failure can lead to a loss of financial support.

The oral examination consists of a 40-minute presentation on the thesis topic, followed by a question period. The questions relate both to the student's presentation and also explore the student's familiarity with broader statistical topics related to the thesis research. The oral examination will normally be completed within the last few months of the student's Ph.D. period. The examining committee usually consists of four faculty members from the Statistics Department and a fifth faculty member from outside the department. Four out of five passing votes are required and no grades are given. Nearly all students can expect to pass this examination, although it is common for specific recommendations to be made regarding completion of the thesis.

A reading committee must also read and approve the thesis. The reading committee will typically be the same as the thesis committee from the thesis proposal meeting.

Transition policy: This is a new scheme that will take effect starting Autumn Quarter 2009-2010. Students who have already passed their Ph.D. proposal defense orals do not need to take the thesis defense oral. Students currently in their first year in 2008-2009 must follow this new policy. Other students currently in second year and beyond can choose either the old or new system; students in this category who choose the new scheme and have already finished their third year can have their initial committee meeting as soon as they are ready.

For further information on University oral examinations and committees, please see the Graduate Academic Policies and Procedures (GAP) Handbook (http://gap.stanford.edu) section 4.7.

Financial Support—Students accepted to the Ph.D. program are offered financial support. All tuition expenses are paid and there is a fixed monthly stipend determined to be sufficient to pay living expenses. Financial support can be continued for five years, department resources permitting, for students in good standing. The resources for student financial support derive from funds made available for student teaching and research assistantships. Students receive both a teaching and research assignment each quarter which, together, do not exceed 20 hours. Students are strongly encouraged to apply for outside scholarships, fellowships, and other forms of financial support.

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