statistics phd coursework

PhD Program information

The Statistics PhD program is rigorous, yet welcoming to students with interdisciplinary interests and different levels of preparation. Students in the PhD program take core courses on the theory and application of probability and statistics during their first year. The second year typically includes additional course work and a transition to research leading to a dissertation. PhD thesis topics are diverse and varied, reflecting the scope of faculty research interests. Many students are involved in interdisciplinary research. Students may also have the option to pursue a designated emphasis (DE) which is an interdisciplinary specialization:  Designated Emphasis in Computational and Genomic Biology ,  Designated Emphasis in Computational Precision Health ,  Designated Emphasis in Computational and Data Science and Engineering . The program requires four semesters of residence.

Normal progress entails:

Year 1 . Perform satisfactorily in preliminary coursework. In the summer, students are required to embark on a short-term research project, internship, graduate student instructorship, reading course, or on another research activity. Years 2-3 . Continue coursework. Find a thesis advisor and an area for the oral qualifying exam. Formally choose a chair for qualifying exam committee, who will also serve as faculty mentor separate from the thesis advisor.  Pass the oral qualifying exam and advance to candidacy by the end of Year 3. Present research at BSTARS each year. Years 4-5 . Finish the thesis and give a lecture based on it in a department seminar.

Program Requirements

• Qualifying Exam

Course work and evaluation

Preliminary stage: the first year.

Effective Fall 2019, students are expected to take four semester-long courses for a letter grade during their first year which should be selected from the core first-year PhD courses offered in the department: Probability (204/205A, 205B,), Theoretical Statistics (210A, 210B), and Applied Statistics (215A, 215B). These requirements can be altered by a member of the PhD Program Committee (in consultation with the faculty mentor and by submitting a graduate student petition ) in the following cases:

• Students primarily focused on probability will be allowed to substitute one semester of the four required semester-long courses with an appropriate course from outside the department.
• Students may request to postpone one semester of the core PhD courses and complete it in the second year, in which case they must take a relevant graduate course in their first year in its place. In all cases, students must complete the first year requirements in their second year as well as maintain the overall expectations of second year coursework, described below. Some examples in which such a request might be approved are described in the course guidance below.
• Students arriving with advanced standing, having completed equivalent coursework at another institution prior to joining the program, may be allowed to take other relevant graduate courses at UC Berkeley to satisfy some or all of the first year requirements

Requirements on course work beyond the first year

Students entering the program before 2022 are required to take five additional graduate courses beyond the four required in the first year, resulting in a total of nine graduate courses required for completion of their PhD. In their second year, students are required to take three graduate courses, at least two of them from the department offerings, and in their third year, they are required to take at least two graduate courses. Students are allowed to change the timing of these five courses with approval of their faculty mentor. Of the nine required graduate courses, students are required to take for credit a total of 24 semester hours of courses offered by the Statistics department numbered 204-272 inclusive. The Head Graduate Advisor (in consultation with the faculty mentor and after submission of a graduate student petition) may consent to substitute courses at a comparable level in other disciplines for some of these departmental graduate courses. In addition, the HGA may waive part of this unit requirement.

Starting with the cohort entering in the 2022-23 academic year , students are required to take at least three additional graduate courses beyond the four required in the first year, resulting in a total of seven graduate courses required for completion of their PhD. Of the seven required graduate courses, five of these courses must be from courses offered by the Statistics department and numbered 204-272, inclusive. With these reduced requirements, there is an expectation of very few waivers from the HGA. We emphasize that these are minimum requirements, and we expect that students will take additional classes of interest, for example on a S/U basis, to further their breadth of knowledge. 

For courses to count toward the coursework requirements students must receive at least a B+ in the course (courses taken S/U do not count, except for STAT 272 which is only offered S/U).  Courses that are research credits, directed study, reading groups, or departmental seminars do not satisfy coursework requirements (for courses offered by the Statistics department the course should be numbered 204-272 to satisfy the requirements). Upper-division undergraduate courses in other departments can be counted toward course requirements with the permission of the Head Graduate Advisor. This will normally only be approved if the courses provide necessary breadth in an application area relevant to the student’s thesis research.

First year course work: For the purposes of satisfactory progression in the first year, grades in the core PhD courses are evaluated as: A+: Excellent performance in PhD program A: Good performance in PhD program A-: Satisfactory performance B+: Performance marginal, needs improvement B: Unsatisfactory performance

First year and beyond: At the end of each year, students must meet with his or her faculty mentor to review their progress and assess whether the student is meeting expected milestones. The result of this meeting should be the completion of the student’s annual review form, signed by the mentor ( available here ). If the student has a thesis advisor, the thesis advisor must also sign the annual review form.

Guidance on choosing course work

Choice of courses in the first year: Students enrolling in the fall of 2019 or later are required to take four semesters of the core PhD courses, at least three of which must be taken in their first year. Students have two options for how to schedule their four core courses:

• Option 1 -- Complete Four Core Courses in 1st year: In this option, students would take four core courses in the first year, usually finishing the complete sequence of two of the three sequences.  Students following this option who are primarily interested in statistics would normally take the 210A,B sequence (Theoretical Statistics) and then one of the 205A,B sequence (Probability) or the 215A,B sequence (Applied Statistics), based on their interests, though students are allowed to mix and match, where feasible. Students who opt for taking the full 210AB sequence in the first year should be aware that 210B requires some graduate-level probability concepts that are normally introduced in 205A (or 204).
• Option 2 -- Postponement of one semester of a core course to the second year: In this option, students would take three of the core courses in the first year plus another graduate course, and take the remaining core course in their second year. An example would be a student who wanted to take courses in each of the three sequences. Such a student could take the full year of one sequence and the first semester of another sequence in the first year, and the first semester of the last sequence in the second year (e.g. 210A, 215AB in the first year, and then 204 or 205A in the second year). This would also be a good option for students who would prefer to take 210A and 215A in their first semester but are concerned about their preparation for 210B in the spring semester.  Similarly, a student with strong interests in another discipline, might postpone one of the spring core PhD courses to the second year in order to take a course in that discipline in the first year.  Students who are less mathematically prepared might also be allowed to take the upper division (under-graduate) courses Math 104 and/or 105 in their first year in preparation for 205A and/or 210B in their second year. Students who wish to take this option should consult with their faculty mentor, and then must submit a graduate student petition to the PhD Committee to request permission for  postponement. Such postponement requests will be generally approved for only one course. At all times, students must take four approved graduate courses for a letter grade in their first year.

After the first year: Students with interests primarily in statistics are expected to take at least one semester of each of the core PhD sequences during their studies. Therefore at least one semester (if not both semesters) of the remaining core sequence would normally be completed during the second year. The remaining curriculum for the second and third years would be filled out with further graduate courses in Statistics and with courses from other departments. Students are expected to acquire some experience and proficiency in computing. Students are also expected to attend at least one departmental seminar per week. The precise program of study will be decided in consultation with the student’s faculty mentor.

Remark. Stat 204 is a graduate level probability course that is an alternative to 205AB series that covers probability concepts most commonly found in the applications of probability. It is not taught all years, but does fulfill the requirements of the first year core PhD courses. Students taking Stat 204, who wish to continue in Stat 205B, can do so (after obtaining the approval of the 205B instructor), by taking an intensive one month reading course over winter break.

Designated Emphasis: Students with a Designated Emphasis in Computational and Genomic Biology or Designated Emphasis in Computational and Data Science and Engineering should, like other statistics students, acquire a firm foundation in statistics and probability, with a program of study similar to those above. These programs have additional requirements as well. Interested students should consult with the graduate advisor of these programs. 

Starting in the Fall of 2019, PhD students are required in their first year to take four semesters of the core PhD courses. Students intending to specialize in Probability, however, have the option to substitute an advanced mathematics class for one of these four courses. Such students will thus be required to take Stat 205A/B in the first year,  at least one of Stat 210A/B or Stat 215A/B in the first year, in addition to an advanced mathematics course. This substitute course will be selected in consultation with their faculty mentor, with some possible courses suggested below. Students arriving with advanced coursework equivalent to that of 205AB can obtain permission to substitute in other advanced probability and mathematics coursework during their first year, and should consult with the PhD committee for such a waiver.

During their second and third years, students with a probability focus are expected to take advanced probability courses (e.g., Stat 206 and Stat 260) to fulfill the coursework requirements that follow the first year. Students are also expected to attend at least one departmental seminar per week, usually the probability seminar. If they are not sufficiently familiar with measure theory and functional analysis, then they should take one or both of Math 202A and Math 202B. Other recommended courses from the department of Mathematics or EECS include:

Math 204, 222 (ODE, PDE) Math 205 (Complex Analysis) Math 258 (Classical harmonic analysis) EE 229 (Information Theory and Coding) CS 271 (Randomness and computation)

The Qualifying Examination 

The oral qualifying examination is meant to determine whether the student is ready to enter the research phase of graduate studies. It consists of a 50-minute lecture by the student on a topic selected jointly by the student and the thesis advisor. The examination committee consists of at least four faculty members to be approved by the department.  At least two members of the committee must consist of faculty from the Statistics and must be members of the Academic Senate. The chair must be a member of the student’s degree-granting program.

Qualifying Exam Chair. For qualifying exam committees formed in the Fall of 2019 or later, the qualifying exam chair will also serve as the student’s departmental mentor, unless a student already has two thesis advisors. The student must select a qualifying exam chair and obtain their agreement to serve as their qualifying exam chair and faculty mentor. The student's prospective thesis advisor cannot chair the examination committee. Selection of the chair can be done well in advance of the qualifying exam and the rest of the qualifying committee, and because the qualifying exam chair also serves as the student’s departmental mentor (unless the student has co-advisors), the chair is expected to be selected by the beginning of the third year or at the beginning of the semester of the qualifying exam, whichever comes earlier. For more details regarding the selection of the Qualifying Exam Chair, see the "Mentoring" tab.  

Paperwork and Application. Students at the point of taking a qualifying exam are assumed to have already found a thesis advisor and to should have already submitted the internal departmental form to the Graduate Student Services Advisor ( found here ).  Selection of a qualifying exam chair requires that the faculty member formally agree by signing the internal department form ( found here ) and the student must submit this form to the Graduate Student Services Advisor.  In order to apply to take the exam, the student must submit the Application for the Qualifying Exam via CalCentral at least three weeks prior to the exam. If the student passes the exam, they can then officially advance to candidacy for the Ph.D. If the student fails the exam, the committee may vote to allow a second attempt. Regulations of the Graduate Division permit at most two attempts to pass the oral qualifying exam. After passing the exam, the student must submit the Application for Candidacy via CalCentral .

The Doctoral Thesis

The Ph.D. degree is granted upon completion of an original thesis acceptable to a committee of at least three faculty members. The majority or at least half of the committee must consist of faculty from Statistics and must be members of the Academic Senate. The thesis should be presented at an appropriate seminar in the department prior to filing with the Dean of the Graduate Division. See Alumni if you would like to view thesis titles of former PhD Students.

Graduate Division offers various resources, including a workshop, on how to write a thesis, from beginning to end. Requirements for the format of the thesis are rather strict. For workshop dates and guidelines for submitting a dissertation, visit the Graduate Division website.

Students who have advanced from candidacy (i.e. have taken their qualifying exam and submitted the advancement to candidacy application) must have a joint meeting with their QE chair and their PhD advisor to discuss their thesis progression; if students are co-advised, this should be a joint meeting with their co-advisors. This annual review is required by Graduate Division.  For more information regarding this requirement, please see  https://grad.berkeley.edu/ policy/degrees-policy/#f35- annual-review-of-doctoral- candidates .

Teaching Requirement

For students enrolled in the graduate program before Fall 2016, students are required to serve as a Graduate Student Instructor (GSI) for a minimum of 20 hours (equivalent to a 50% GSI appointment) during a regular academic semester by the end of their third year in the program.

Effective with the Fall 2016 entering class, students are required to serve as a GSI for a minimum of two 50% GSI appointment during the regular academic semesters prior to graduation (20 hours a week is equivalent to a 50% GSI appointment for a semester) for Statistics courses numbered 150 and above. Exceptions to this policy are routinely made by the department.

Each spring, the department hosts an annual conference called BSTARS . Both students and industry alliance partners present research in the form of posters and lightning talks. All students in their second year and beyond are required to present a poster at BSTARS each year. This requirement is intended to acclimate students to presenting their research and allow the department generally to see the fruits of their research. It is also an opportunity for less advanced students to see examples of research of more senior students. However, any students who do not yet have research to present can be exempted at the request of their thesis advisor (or their faculty mentors if an advisor has not yet been determined).

Mentoring for PhD Students

Initial Mentoring: PhD students will be assigned a faculty mentor in the summer before their first year. This faculty mentor at this stage is not expected to be the student’s PhD advisor nor even have research interests that closely align with the student. The job of this faculty mentor is primarily to advise the student on how to find a thesis advisor and in selecting appropriate courses, as well as other degree-related topics such as applying for fellowships.  Students should meet with their faculty mentors twice a semester. This faculty member will be the designated faculty mentor for the student during roughly their first two years, at which point students will find a qualifying exam chair who will take over the role of mentoring the student.

Research-focused mentoring : Once students have found a thesis advisor, that person will naturally be the faculty member most directly overseeing the student’s progression. However, students will also choose an additional faculty member to serve as a the chair of their qualifying exam and who will also serve as a faculty mentor for the student and as a member of his/her thesis committee. (For students who have two thesis advisors, however, there is not an additional faculty mentor, and the quals chair does NOT serve as the faculty mentor).

The student will be responsible for identifying and asking a faculty member to be the chair of his/her quals committee. Students should determine their qualifying exam chair either at the beginning of the semester of the qualifying exam or in the fall semester of the third year, whichever is earlier. Students are expected to have narrowed in on a thesis advisor and research topic by the fall semester of their third year (and may have already taken qualifying exams), but in the case where this has not happened, such students should find a quals chair as soon as feasible afterward to serve as faculty mentor.

Students are required to meet with their QE chair once a semester during the academic year. In the fall, this meeting will generally be just a meeting with the student and the QE chair, but in the spring it must be a joint meeting with the student, the QE chair, and the PhD advisor. If students are co-advised, this should be a joint meeting with their co-advisors.

If there is a need for a substitute faculty mentor (e.g. existing faculty mentor is on sabbatical or there has been a significant shift in research direction), the student should bring this to the attention of the PhD Committee for assistance.

PhD Student Forms:

Important milestones: .

Each of these milestones is not complete until you have filled out the requisite form and submitted it to the GSAO. If you are not meeting these milestones by the below deadline, you need to meet with the Head Graduate Advisor to ask for an extension. Otherwise, you will be in danger of not being in good academic standing and being ineligible for continued funding (including GSI or GSR appointments, and many fellowships). 

†Students who are considering a co-advisor, should have at least one advisor formally identified by the end of the second year; the co-advisor should be identified by the end of the fall semester of the 3rd year in lieu of finding a Research Mentor/QE Chair.

Expected Progress Reviews: 

* These meetings do not need to be held in the semester that you take your Qualifying Exam, since the relevant people should be members of your exam committee and will discuss your research progress during your qualifying exam

** If you are being co-advised by someone who is not your primary advisor because your primary advisor cannot be your sole advisor, you should be meeting with that person like a research mentor, if not more frequently, to keep them apprised of your progress. However, if both of your co-advisors are leading your research (perhaps independently) and meeting with you frequently throughout the semester, you do not need to give a fall research progress report.

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The Ph.D. in Statistics is flexible and allows students to pursue a variety of directions, ranging from statistical methodology and interdisciplinary research to theoretical statistics and probability theory. Students typically start the Ph.D. program by taking courses and gradually transition to research that will ultimately lead to their dissertation, the most important component of the Ph.D. program.

These requirements apply to students admitted for Fall 2020 and after. Students admitted in Fall 2019 and earlier should consult the Previous Program Requirements page .

PhD Coursework:

The core PhD curriculum is divided into five areas: 

Methods — STATS 600 and 601

Practice — STATS 604

Statistical Theory — STATS 511, 610, 611

Probability — STATS 510, 620, 621

Computing — STATS 507, 606, 608 

All doctoral students must complete the following in their first three semesters in the program and before advancing to candidacy: 

Take all methods and practice courses (600, 601, 604)

Take at least two courses in the combined areas of statistical theory and probability,  including at least one course in statistical theory and at least one 600-level course 

Take at least one computing course

Achieve a 3.5 average grade  (on the 4.0 scale used by Rackham) in 600, 601, 604, and one 600-level statistical theory or probability course

Not completing requirements 1-4 by the end of the third semester will trigger probation which, if not resolved by the end of the fourth semester, may lead to dismissal from the program.  For more details, see the link below. 

By the end of the PhD program, all students must take at least 30 credits of graduate statistics courses.    All courses from the core areas count towards this total, as well as all 600-level, 700-level, and selected additional  500-level courses with approval of the PhD Program Director. Seminars and independent study courses do not count. At least 21 credits must be at the 600 level or higher.    The Rackham Graduate School requires PhD students to maintain an overall GPA of at least 3.0 to remain in good standing.   

In addition, all doctoral  students must take 3 credits of cognate courses as required by the Rackham graduate school, and two professional development seminar courses.    Cognate courses are 400- and higher-level courses from outside Statistics and not cross-listed with Statistics. All cognate course selections must be approved by the PhD Program Director.   The professional development courses are 

STATS 810, research ethics and introduction to research tools, in the first semester in the program.

STATS 811, technical writing in statistics. Students are strongly advised to complete this course in their second or third year.

Typical Course Schedules:

Our Ph.D. program admits students with diverse academic backgrounds. All PhD students take STATS 600/601  in their first year. Students are strongly encouraged to take STATS 604 in their second year (Stats 600 is a prerequisite).  

Students with less mathematical preparation typically take STATS 510/511 (the Master’s level probability and statistical theory) in their first year and 600-level probability and/or statistical theory courses in their second year.    

Advanced students, for example those with a Master’s degree, typically do not need to take 510/511, and in some cases may skip 610 and 621.   Students who wish to take 600-level probability and statistical theory courses in their first year must take a placement test just before the fall semester of their first year to get approved.  The PhD Program Director will help each student choose their individual path towards completing the requirements.  

Some typical sample schedules are listed below.   In most cases, we do not recommend taking more than three full-load courses per semester (not counting seminars).

Sample schedule 1:

Sample schedule 2:

Advancing to Candidacy:

Students are expected to find a faculty advisor and start research leading to their dissertation proposal no later than the summer after their first year. The PhD Program Director and the faculty mentor assigned to each first year student can assist with finding a faculty advisor. Students are expected to submit a dissertation proposal and advance to candidacy some time during their second or third year in the program.   

Requirements for advancing to candidacy are:

Satisfying Requirements 1-4

Completing at least 3 credit hours of cognate courses

Writing a dissertation proposal and passing the oral preliminary exam, which consists of presenting the proposal to the student's preliminary thesis committee

A dissertation proposal should identify an interesting research problem, provide motivation for studying it, review the relevant literature, propose an approach for solving the problem​, and present at least some preliminary results​. The written proposal must be submitted to the preliminary thesis committee and the graduate coordinator a​head of time (one week minimum, two weeks recommended)​ and then presented in the oral preliminary exam. The preliminary thesis committee is chaired by the faculty advisor and must include at least two more faculty members, at least one of them from Statistics. ​​The faculty on the preliminary thesis committee typically continue t​o serve ​on ​the doctoral thesis committee​​, but changes are allowed.  Please see Rackham rules on thesis committees for more information.  

At the oral preliminary exam, the committee will ask questions about the proposal and the relevant background and either elect to accept the proposal as both substantial and feasible, ask for specific revisions, or decline the proposal. The unanimous approval of the proposal by the committee is necessary for the student to advance to candidacy.

Additional Information:

Students are encouraged to complete the bulk of their coursework beyond Requirements 1-4 in the first two years of study.  Candidates are allowed to take only one course per semester without an increase in tuition.

All PhD students are expected to register for Stats 808/809  (Department Seminar) every semester unless restricted by candidacy, and attend the seminar regularly regardless of whether they are registered.  

Exceptions to the PhD program requirements may be granted by the PhD Program Director.

Annual Report:

Each candidate is required to meet with the members of their thesis committee annually. This could be in the form of either giving a short presentation on their research progress to the thesis committee as a group, or meeting with committee members individually.

Each committee member should complete a Thesis Committee Member Report and return it to the student. The student should share the completed Thesis Committee Member Reports with both the PhD Program Coordinator and their advisor.

All meetings with the committee members should take place by April 15.

Following the meetings, the student and the advisor should complete the Annual PhD Candidate Self-Evaluation and Feedback Form . The advisor should review the committee members’ Thesis Committee Member Reports and take them into account when completing the advisor’s portion. The completed Annual PhD Candidate Self-Evaluation and Advisor Feedback Form must be submitted to the PhD Program Coordinator by May 31. The completed form will be saved with the department, and a copy will be shared with the student.

Dissertation and Defense:

Each doctoral student is expected to write a dissertation that makes a substantial and original contribution to statistics or a closely related field. This is the most important element of the doctoral program. After advancing to candidacy, students are expected to focus on their thesis research under the supervision of the thesis advisor and the doctoral committee. The composition of the doctoral committee must follow the Rackham's  guidelines for dissertation committee service . The written dissertation is submitted to the committee for evaluation and presented in an oral defense open to the public.

Rackham Requirements:

The Rackham Graduate School imposes some additional requirements concerning residency, fees, and time limits. Students are expected to know and comply with these requirements.

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The department encourages research in both theoretical and applied statistics. Faculty members of the department have been leaders in research on a multitude of topics that include statistical inference, statistical computing and Monte-Carlo methods, analysis of missing data, causal inference, stochastic processes, multilevel models, experimental design, network models and the interface of statistics and the social, physical, and biological sciences. A unique feature of the department lies in the fact that apart from methodological research, all the faculty members are also heavily involved in applied research, developing novel methodology that can be applied to a wide array of fields like astrophysics, biology, chemistry, economics, engineering, public policy, sociology, education and many others.

Two carefully designed special courses offered to Ph.D. students form a unique feature of our program. Among these, Stat 303 equips students with the  basic skills necessary to teach statistics , as well as to be better overall statistics communicators. Stat 399 equips them with generic skills necessary for problem solving abilities.

Our Ph.D. students often receive substantial guidance from several faculty members, not just from their primary advisors, and in several settings. For example, every Ph.D. candidate who passes the qualifying exam gives a 30 minute presentation each semester (in Stat 300 ), in which the faculty ask questions and make comments. The Department recently introduced an award for Best Post-Qualifying Talk (up to two per semester), to further encourage and reward inspired research and presentations.

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Statistics-PhD Coursework

*The below list of requirements are for those students admitted to Fall 2021 or after. Students admitted prior to Fall 2021 are allowed to follow the below list or the previous program requirements .  

Prerequisites

• MATH 447 - Real Variables (*Waived if a course at an equivalent level has been taken at another institution and a grade of B or above is achieved)

Required courses:

PhD applied regression courses  (8 hours) 

• STAT 527 - Advanced Regression Analysis I (4 hours) - Qualifying Exam Course
• STAT 528 - Advanced Regression Analysis II (4 hours) - Qualifying Exam Course

PhD theory core courses (12 hours)

• STAT 511 - Advanced Mathematical Statistics (4 hours) - Qualifying Exam Course
• STAT 575 - Large sample theory (4 hours) - Qualifying Exam Course
• STAT 553 - Probability and Measure I (4 hours)

Practicum course: select one (0-4 hours)

• STAT 427 - Statistical Consulting (4 hours)
• STAT 593 - Internship (0-4 hours)
• STAT 595 - Preparing Future Faculty (2 hours)

Computing-related course: select one (4 hours)

• STAT 525 - Computational Statistics (4 hours)
• STAT 542 - Statistical Learning (4 hours)
• IE 521 - Convex Optimization (4 hours)
• IE 534 - Deep Learning (4 hours)
• CS 573 - Algorithms (4 hours)
• CS 574 - Randomized Algorithms (4 hours)
• CS 583 - Approximation Algorithms (4 hours)

Stochastic Processes and Time Series courses: select one (4 hours)

• STAT 556 - Advanced Time Series Analysis (4 hours)
• STAT 555/MATH 564 - Applied Stochastic Processes (4 hours)
• STAT 533 – Advanced Stochastic Processes (4 hours)
• STAT 554 - Probability and Measure II (4 hours)
• STAT 576 - Weak Convergence and Empirical Processes (4 hours)

Select at least five elective courses with at least three 500 levels, not selected above (20 hours)

• STAT 428 - Statistical Computing (4 hours)
• STAT 429 - Time Series Analysis (4 hours)
• STAT 431 – Applied Bayesian Analysis (4 hours)
• STAT 433 - Stochastic processes (4 hours)
• STAT 434 - Survival Analysis (4 hours)
• STAT 437 - Unsupervised Learning (4 hours)
• STAT 448 - Advanced Data Analysis (4 hours)
• STAT 466 - Image and Neuroimage Analysis (4 hours)
• STAT 480 - Big Data Analytics (4 hours)
• STAT 530 - Bioinformatics (4 hours)
• STAT 534 – Advanced Survival Analysis (4 hours)
• STAT 538 - Clinical Trials Methodology (4 hours)
• STAT 545 – Spatial Statistics (4 hours)
• STAT 546 – Machine Learning in Data Science (4 hours)
• STAT 551 - Theory of Probability I (4 hours)
• STAT 552 - Theory of Probability II (4 hours)
• STAT 555 - Applied Stochastic Processes (4 hours)
• STAT 571 - Multivariate Analysis (4 hours)
• STAT 578 - Topics in Statistics (4 hours)
• STAT 587 - Hierarchical Linear Models (4 hours)
• STAT 588 - Covariance Structures and Factor Models (4 hours)

Approved elective courses offered by other departments (other courses subject to approval by the PhD committee)

• CS 512 - Data Mining Principles
• CS 543 - Computer Vision
• CS 546 - Machine Learning in NLP
• CS 573 - Algorithms
• CS 583 - Approximation Algorithms
• ECE 547 - Topics in Image Processing
• ECE 561 - Detection and Estimation Theory
• ECE 563 - Information Theory
• ECE 566 - Computational Inference and Learning
• ECE 580 - Optimization by Vector Space Methods
• ECON 536 - Applied Econometrics
• ECON 574 - Econometrics I
• ECON 575 - Econometrics II
• ECON 576 - Time Series
• ECON 590 - Applied Macroeconometrics
• ECON 590 - Applied Financial Econometrics
• IE 510 - Applied Nonlinear Programming
• IE 521 - Convex Optimization
• IE 528 - Computing for Data Analytics
• IE 529 - Stats of Big Data & Clustering
• MATH 540 - Real Analysis
• MATH 580 - Combinatorial Mathematics
• MATH 585 - Probabilistic Combinatorics
• MATH 588 - Optimization in Networks
• MATH 589 - Conjugate Duality and Optimization

Thesis and Individual study courses

• STAT 590 - Individual Study and Research (0-16 hours, repeatable)
• STAT 599 - Thesis Research (0-8 hours, repeatable) 

Total Hours: 96 Credit Hours for Stage 1 Admit; 64 Credit Hours for Stage 2 Admit

Entering with an approved Baccalaureate degree (Stage 1) The above requirement applies. At least 52 required and elective course credits at UIUC. Thesis research and individual study courses (min-max applied toward degree): 0-44 A student cannot deposit a thesis without record of registration in thesis research credit (599)

Total number of credits required: 96 (at least 64 residency credits)

Entering with an approved Master degree (Stage 2) Entering with an approved MS degree in Statistics or related field from peer institution will make student eligible to waive STAT 527/STAT 528/STAT 511/STAT 575 (Qualifying Exam courses). PhD committee must approve prior degree after admission and before Sept. 1st of the first term of enrollment. Student must still pass Qualifying Exam after first year of enrollment. At least 32 required and elective course credits at UIUC. Thesis research and individual study courses (min-max applied toward degree): 0-32. A student cannot deposit a thesis without record of registration in thesis research credit (599)

Total number of credits required: 64

Other Requirements: Other requirements may overlap

• Minimum 500-level hours required: 24
• Qualifying Exam: Yes
• Preliminary Exam: Yes
• Final Exam/Dissertation Defense: Yes
• Dissertation Deposit: Yes
• Minimum GPA: 3.0

PhD Program

Advanced undergraduate or masters level work in mathematics and statistics will provide 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 has expanded its research and educational activities towards computational biology, mathematical finance and information science. The doctoral program normally takes four to five years to complete.

Doctoral Program in Statistics

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PhD in Statistics

Program description.

The Ph.D. program in statistics prepares students for a career pursuing research in either academia or industry.  The program provides rigorous classroom training in the theory, methodology, and application of statistics, and provides the opportunity to work with faculty on advanced research topics over a wide range of theory and application areas. To enter, students need a bachelor’s degree in mathematics, statistics, or a closely related discipline. Students graduating with a PhD in Statistics are expected to:

• Demonstrate an understanding the core principles of Probability Theory, Estimation Theory, and Statistical Methods.
• Demonstrate the ability to conduct original research in statistics.
• Demonstrate the ability to present research-level statistics in a formal lecture

Requirements for the Ph.D. (Statistics Track)

Course Work A Ph.D. student in our department must complete sixteen courses for the Ph.D. At most, four of these courses may be transferred from another institution. If the Ph.D. student is admitted to the program at the post-Master’s level, then eight courses are usually required.

Qualifying Examinations First, all Ph.D. students in the statistics track must take the following two-semester sequences: MA779 and MA780 (Probability Theory I and II), MA781 (Estimation Theory) and MA782 (Hypothesis Testing), and MA750 and MA751 (Advanced Statistical Methods I and II). Then, to qualify a student to begin work on a PhD dissertation, they must pass two of the following three exams at the PhD level: probability, mathematical statistics, and applied statistics. The probability and mathematical statistics exams are offered every September and the applied statistics exam is offered every April.

• PhD Exam in Probability: This exam covers the material covered in MA779 and MA780 (Probability Theory I and II).
• PhD Exam in Mathematical Statistics: This exam covers material covered in MA781 (Estimation Theory) and MA782 (Hypothesis Testing).
• PhD Exam in Applied Statistics: This exam covers the same material as the M.A. Applied exam and is offered at the same time, except that in order to pass it at the PhD level a student must correctly solve all four problems.

Note: Students concentrating in probability may choose to do so either through the statistics track or through the mathematics track. If a student wishes to do so through the mathematics track, the course and exam requirements are different. Details are available here .

Dissertation The dissertation is the major requirement for a Ph.D. student. After the student has completed all course work, the Director of Graduate Studies, in consultation with the student, selects a three-member dissertation committee. One member of this committee is designated by the Director of Graduate Studies as the Major Advisor for the student. Once completed, the dissertation must be defended in an oral examination conducted by at least five members of the Department.

The Dissertation and Final Oral Examination follows the   GRS General Requirements for the Doctor of Philosophy Degree .

Satisfactory Progress Toward the Degree Upon entering the graduate program, each student should consult the Director of Graduate Studies (Prof. David Rohrlich) and the Associate Director of the Program in Statistics (Prof. Konstantinos Spiliopoulos). Initially, the Associate Director of the Program in Statistics will serve as the default advisor to the student. Eventually the student’s advisor will be determined in conjunction with their dissertation research. The Associate Director of the Program in Statistics, who will be able to guide the student through the course selection and possible directed study, should be consulted often, as should the Director of Graduate Studies. Indeed, the Department considers it important that each student progress in a timely manner toward the degree. Each M.A. student must have completed the examination by the end of their second year in the program, while a Ph.D. student must have completed the qualifying examination by the third year. Students entering the Ph.D. program with an M.A. degree must have completed the qualifying examination by October of the second year. Failure to meet these deadlines may jeopardize financial aid. Some flexibility in the deadlines is possible upon petition to the graduate committee in cases of inadequate preparation.

Students enrolled in the Graduate School of Arts & Sciences (GRS) are expected to adhere to a number of policies at the university, college, and departmental levels. View the policies on the Academic Bulletin and GRS website .

Residency Post-BA students must complete all of the requirements for a Ph.D. within seven years of enrolling in the program and post-MA students must complete all requirements within five years. This total time limit is set by the Graduate School. Students needing extra time must petition the Graduate School. Also, financial aid is not guaranteed after the student’s fifth year in the program.

Financial Aid

As with all Ph.D. students in the Department of Mathematics and Statistics, the main source of financial aid for graduate students studying statistics is a Teaching Fellowship. These awards carry a stipend as well as tuition remission for six courses per year. Teaching Fellows are required to assist a faculty member who is teaching a course, usually a large lecture section of an introductory statistics course. Generally, the Teaching Fellow is responsible for conducting a number of discussion sections consisting of approximately twenty-five students each, as well as for holding office hours and assisting with grading. The Teaching Fellowship usually entails about twenty hours of work per week. For that reason, Teaching Fellows enroll in at most three courses per semester. A Teaching Fellow Seminar is conducted to help new Teaching Fellows develop as instructors and to promote the continuing development of experienced Teaching Fellows.

Other sources of financial aid include University Fellowships and Research Assistantships. The University Fellowships are one-year awards for outstanding students and are service-free. They carry stipends plus full tuition remission. Students do not need to apply for these fellowships. Research Assistantships are linked to research done with individual faculty, and are paid for through those faculty members’ grants. As a result, except on rare occasions, Research Assistantships typically are awarded to students in their second year and beyond, after student and faculty have had sufficient time to determine mutuality of their research interests.

Regular reviews of the performance of Teaching Fellows and Research Assistants in their duties as well as their course work are conducted by members of the Department’s Graduate Committee.

Ph.D. Program Milestones

The department considers it essential that each student progress in a timely manner toward completion of the degree. The following are the deadlines for achieving the milestones described in the Degree Requirements and constitute the basis for evaluating satisfactory progress towards the Ph.D. These deadlines are not to be construed as expected times to complete the various milestones, but rather as upper bounds. In other words,   a student in good standing expecting to complete   the degree within the five years of guaranteed funding will meet these milestones by the much e arlier target dates indicated below.   Failure to achieve these milestones in a timely manner may affectfinancial aid.

• Target: April of Year 1
• Deadline: April of Year 2
• Target: Spring of Year 2 post-BA/Spring of Year 1 post-MA
• Deadline: End of Year 3 post-BA/Fall of Year 2 post-MA
• Target: Spring of Year 2
• Deadline: End of Year 3
• Target: Spring of Year 2 or Fall of Year 3 post-BA/October of Year 2 post-MA
• Deadline: End of Year 3 post-BA/October of Year 2 post-MA
• Target: end of Year 3
• Deadline: End of Year 4
• Target: End of Year 5
• Deadline: End of Year 6

If you have any questions regarding our PhD program in Statistics, please reach out to us at [email protected]

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PhD Program

Wharton’s PhD program in Statistics provides the foundational education that allows students to engage both cutting-edge theory and applied problems. These include problems from a wide variety of fields within Wharton, such as finance, marketing, and public policy, as well as fields across the rest of the University such as biostatistics within the Medical School and computer science within the Engineering School.

Major areas of departmental research include: analysis of observational studies; Bayesian inference, bioinformatics; decision theory; game theory; high dimensional inference; information theory; machine learning; model selection; nonparametric function estimation; and time series analysis.

Students typically have a strong undergraduate background in mathematics. Knowledge of linear algebra and advanced calculus is required, and experience with real analysis is helpful. Although some exposure to undergraduate probability and statistics is expected, skills in mathematics and computer science are more important. Graduates of the department typically take positions in academia, government, financial services, and bio-pharmaceutical industries.

Apply online here .

Department of Statistics and Data Science

The Wharton School, University of Pennsylvania Academic Research Building 265 South 37th Street, 3rd & 4th Floors Philadelphia, PA 19104-1686

Phone: (215) 898-8222

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Department of Technology, Operations, and Statistics | Doctoral Program in Statistics

Doctoral program in statistics.

• Program of Study

Program Requirements

• Doctoral Students and Their Research
• Statistics Faculty

Overview of the Doctoral Program in Statistics

The world’s financial markets produce an enormous stream of data, and the understanding of the techniques needed to analyze and extract information from this stream has become critical.   Doctoral work in statistics combines theory and methodology to deal with the large quantity of statistical data.  Here at Stern we use the theoretical and methodological orientation of a traditional statistics with a focus on the applications that are central to the concerns of a business school.  The PhD thesis work at Stern is a mathematically sophisticated enterprise that never loses sight of the real and practical problems of business.

Stern’s curriculum in statistics prepares students for academic positions by preparing them to conduct independent research.  The statistician must be knowledgeable of the basic issues of the intellectual areas in which his or her work will be applied. 

The most popular areas of student interest in the last few years have been mathematical finance, statistical modeling, data mining, stochastic processes, and econometrics.

Students have rigorous course work and participate in special topics seminars.  They work closely with the faculty and also present special PhD student seminars.

Clifford Hurvich Coordinator, Statistics Doctoral Program

Mission Our mission is the education of scholars who will produce first-rate statistics research and who will succeed as faculty members at first-rate universities.

Admissions and performance We enroll one or two students each year;  these are chosen from approximately 100 highly qualified applicants.

Advising and evaluation Each student will meet with a committee of faculty members yearly to assess progress through the program.

Research and interaction with faculty The Stern statistics faculty have a wide range of interests, but there is special emphasis on time series, statistical modeling, stochastic processes, and financial modeling.

PhD students in statistics take courses in statistical inference, stochastic processes, time series, regression analysis, and multivariate analysis.

In addition to course work, doctoral students also participate in research projects in conjunction with faculty members.  The students attend seminars, present seminars on their own work, and submit their work for publication.

The program culminates with the creation of the PhD thesis, through the stages of proposal, writing, and defense.

Most students finish in four to five years.

Statistics Program of Study

Statistics PhD students take their course work in the first two years of study.  These courses are taken within the Statistics Group (both as formal courses and also as independent study), within other departments at the Stern School, at NYU's Courant Institute, and at Columbia University.

In addition to their statistics courses, doctoral students in Statistics often take courses in mathematics, finance, market research, and econometrics.  The individual curriculum will be planned with the help of faculty advisers.

Questions about the PhD Program in Statistics?

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Cornell University does not offer a separate Masters of Science (MS) degree program in the field of Statistics. Applicants interested in obtaining a masters-level degree in statistics should consider applying to Cornell's MPS Program in Applied Statistics.

Choosing a Field of Study

There are many graduate fields of study at Cornell University. The best choice of graduate field in which to pursue a degree depends on your major interests. Statistics is a subject that lies at the interface of theory, applications, and computing. Statisticians must therefore possess a broad spectrum of skills, including expertise in statistical theory, study design, data analysis, probability, computing, and mathematics. Statisticians must also be expert communicators, with the ability to formulate complex research questions in appropriate statistical terms, explain statistical concepts and methods to their collaborators, and assist them in properly communicating their results. If the study of statistics is your major interest then you should seriously consider applying to the Field of Statistics.

There are also several related fields that may fit even better with your interests and career goals. For example, if you are mainly interested in mathematics and computation as they relate to modeling genetics and other biological processes (e.g, protein structure and function, computational neuroscience, biomechanics, population genetics, high throughput genetic scanning), you might consider the Field of Computational Biology . You may wish to consider applying to the Field of Electrical and Computer Engineering if you are interested in the applications of probability and statistics to signal processing, data compression, information theory, and image processing. Those with a background in the social sciences might wish to consider the Field of Industrial and Labor Relations with a major or minor in the subject of Economic and Social Statistics. Strong interest and training in mathematics or probability might lead you to choose the Field of Mathematics . Lastly, if you have a strong mathematics background and an interest in general problem-solving techniques (e.g., optimization and simulation) or applied stochastic processes (e.g., mathematical finance, queuing theory, traffic theory, and inventory theory) you should consider the Field of Operations Research .

Residency Requirements

Students admitted to PhD program must be "in residence" for at least four semesters, although it is generally expected that a PhD will require between 8 and 10 semesters to complete. The chair of your Special Committee awards one residence unit after the satisfactory completion of each semester of full-time study. Fractional units may be awarded for unsatisfactory progress.

Your Advisor and Special Committee

The Director of Graduate Studies is in charge of general issues pertaining to graduate students in the field of Statistics. Upon arrival, a temporary Special Committee is also declared for you, consisting of the Director of Graduate Studies (chair) and two other faculty members in the field of Statistics. This temporary committee shall remain in place until you form your own Special Committee for the purposes of writing your doctoral dissertation. The chair of your Special Committee serves as your primary academic advisor; however, you should always feel free to contact and/or chat with any of the graduate faculty in the field of Statistics.

The formation of a Special Committee for your dissertation research should serve your objective of writing the best possible dissertation. The Graduate School requires that this committee contain at least three members that simultaneously represent a certain combination of subjects and concentrations. The chair of the committee is your principal dissertation advisor and always represents a specified concentration within the subject & field of Statistics. The Graduate School additionally requires PhD students to have at least two minor subjects represented on your special committee. For students in the field of Statistics, these remaining two members must either represent (i) a second concentration within the subject of Statistics, and one external minor subject; or, (ii) two external minor subjects. Each minor advisor must agree to serve on your special committee; as a result, the identification of these minor members should occur at least 6 months prior to your A examination.

Some examples of external minors include Computational Biology, Demography, Computer Science, Economics, Epidemiology, Mathematics, Applied Mathematics and Operations Research. The declaration of an external minor entails selecting (i) a field other than Statistics in which to minor; (ii) a subject & concentration within the specified field; and, (iii) a minor advisor representing this field/subject/concentration that will work with you in setting the minor requirements. Typically, external minors involve gaining knowledge in 3-5 graduate courses in the specified field/subject, though expectations can vary by field and even by the choice of advisor. While any choice of external minor subject is technically acceptable, the requirement that the minor representative serve on your Special Committee strongly suggests that the ideal choice(s) should share some natural connection with your choice of dissertation topic.

The fields, subjects and concentrations represented on your committee must be officially recognized by the Graduate School ; the Degrees, Subjects & Concentrations tab listed under each field of study provides this information. Information on the concentrations available for committee members chosen to represent the subject of Statistics can be found on the Graduate School webpage . 

Statistics PhD Travel Support

The Department of Statistics and Data Science has established a fund for professional travel for graduate students. The intent of the Department is to encourage travel that enhances the Statistics community at Cornell by providing funding for graduate students in statistics that will be presenting at conferences. Please review the Graduate Student Travel Award Policy website for more information. 

Completion of the PhD Degree

In addition to the specified residency requirements, students must meet all program requirements as outlined in Program Course Requirements and Timetables and Evaluations and Examinations, as well as complete a doctoral dissertation approved by your Special Committee. The target time to PhD completion is between 4 and 5 years; the actual time to completion varies by student.

Students should consult both the Guide to Graduate Study and Code of Legislation of the Graduate Faculty (available at www.gradschool.cornell.edu ) for further information on all academic and procedural matters pertinent to pursuing a graduate degree at Cornell University.

Ph.D. in Statistics

Our doctoral program in statistics gives future researchers preparation to teach and lead in academic and industry careers.

Program Description

Degree type.

approximately 5 years

The relatively new Ph.D. in Statistics strives to be an exemplar of graduate training in statistics. Students are exposed to cutting edge statistical methodology through the modern curriculum and have the opportunity to work with multiple faculty members to take a deeper dive into special topics, gain experience in working in interdisciplinary teams and learn research skills through flexible research electives. Graduates of our program are prepared to be leaders in statistics and machine learning in both academia and industry.

The Ph.D. in Statistics is expected to take approximately five years to complete, and students participate as full-time graduate students.  Some students are able to finish the program in four years, but all admitted students are guaranteed five years of financial support.  

Within our program, students learn from global leaders in statistics and data sciences and have:

20 credits of required courses in statistical theory and methods, computation, and applications

18 credits of research electives working with two or more faculty members, elective coursework (optional), and a guided reading course

Dissertation research

Coursework Timeline

Year 1: focus on core learning.

The first year consists of the core courses:

• SDS 384.2 Mathematical Statistics I
• SDS 383C Statistical Modeling I
• SDS 387 Linear Models
• SDS 384.11 Theoretical Statistics
• SDS 383D Statistical Modeling II
• SDS 386D Monte Carlo Methods

In addition to the core courses, students of the first year are expected to participate in SDS 190 Readings in Statistics. This class focuses on learning how to read scientific papers and how to grasp the main ideas, as well as on practicing presentations and getting familiar with important statistics literature.

At the end of the first year, students are expected to take a written preliminary exam. The examination has two purposes: to assess the student’s strengths and weaknesses and to determine whether the student should continue in the Ph.D. program. The exam covers the core material covered in the core courses and it consists of two parts: a 3-hour closed book in-class portion and a take-home applied statistics component. The in-class portion is scheduled at the end of the Spring Semester after final exams (usually late May). The take-home problem is distributed at the end of the in-class exam, with a due-time 24 hours later. 

Year 2: Transitioning from Student to Researcher

In the second year of the program, students take the following courses totaling 9 credit hours each semester:

• Required: SDS 190 Readings in Statistics (1 credit hour)
• Required: SDS 389/489 Research Elective* (3 or 4 credit hours) in which the student engages in independent research under the guidance of a member of the Statistics Graduate Studies Committee
• One or more elective courses selected from approved electives ; and/or
• One or more sections of SDS 289/389/489 Research Elective* (2 to 4 credit hours) in which the student engages in independent research with a member(s) of the Statistics Graduate Studies Committee OR guided readings/self-study in an area of statistics or machine learning. 
• Internship course (0 or 1 credit hour; for international students to obtain Curricular Practical Training; contact Graduate Coordinator for appropriate course options)
• GRS 097 Teaching Assistant Fundamentals or NSC 088L Introduction to Evidence-Based Teaching (0 credit hours; for TA and AI preparation)

* Research electives allow students to explore different advising possibilities by working for a semester with a particular professor. These projects can also serve as the beginning of a dissertation research path. No more than six credit hours of research electives can be taken with a single faculty member in a semester.

Year 3: Advance to Candidacy

Students are encouraged to attend conferences, give presentations, as well as to develop their dissertation research. At the end of the second year or during their third year, students are expected to present their plan of study for the dissertation in an Oral candidacy exam. During this exam, students should demonstrate their research proficiency to their Ph.D. committee members. Students who successfully complete the candidacy exam can apply for admission to candidacy for the Ph.D. once they have completed their required coursework and satisfied departmental requirements. The steps to advance to candidacy are:

• Discuss potential candidacy exam topics with advisor
• Propose Ph.D. committee: the proposed committee must follow the Graduate School and departmental regulations on committee membership for what will become the Ph.D. Dissertation Committee
•   Application for candidacy

Year 4+: Dissertation Completion and Defense

Students are encouraged to attend conferences, give presentations, as well as to develop their dissertation research. Moreover, they are expected to present part of their work in the framework of the department's Ph.D. poster session.

Students who are admitted to candidacy will be expected to complete and defend their Ph.D. thesis before their Ph.D. committee to be awarded the degree. The final examination, which is oral, is administered only after all coursework, research and dissertation requirements have been fulfilled. It is expected that students will be prepared to defend by the end of their fifth year in the doctoral program.

General Information and Expectations for All Ph.D. students

• 2023-24 Student Handbook
• Annual Review At the end of every year (due May 1), students are expected to fill out the Annual Progress Review . 
• Seminar Series All students are expected to attend the SDS Seminar Series
• SDS 189R Course Description (when taken for internship)
• Internship Course Registration form
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Attending Conferences 

Students are encouraged to attend conferences to share their work. All research-related travel while in student status require prior authorization.

• Request for Travel Authorization (both domestic and international travel)
• Request for Authorization for International Travel  

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This program has a rich tradition of creating groundbreaking statistical methods and conducting innovative applied statistics, bridging theory and practice and supporting knowledge discovery and decision-making through meaningful data extraction and analysis. Statistics is an indispensable pillar of modern science, including data science and artificial intelligence.

You can take advantage of the department’s flexible research options and work with your faculty of choice. You can leverage cross-department collaboration with biology, chemistry, medical sciences, economics, computer science, government, and public health to pursue your intellectual interests. You will become part of a close-knit, friendly department that offers many extra learning opportunities both inside and outside the program.

Examples of student projects include developing statistical methods to forecast infectious diseases from online search data, delineating causality from association, building a software package for evaluating redistricting plans in 50 states, leveraging machine learning algorithms for model-free inference, and employing a randomization-based inference framework to study peer effects. 

Graduates have secured faculty positions in institutions such as Stanford University; University of Pennsylvania; University of California, Berkeley; Johns Hopkins University; Carnegie Mellon University; Columbia University; and Georgia Institute of Technology. Others have begun careers at organizations such as Google, Apple, Etsy, Citadel, and the Boston Red Sox. 

Additional information on the graduate program is available from the Department of Statistics , and requirements for the degree are detailed in Policies .

Admissions Requirements

Please review admissions requirements and other information before applying. You can find degree program-specific admissions requirements below and access additional guidance on applying from the Department of Statistics .

Academic Background

Applicants should understand what the discipline of statistics entails and show evidence of involvement in applications or a strong theoretical interest.

The minimum mathematical preparation for admission is linear algebra and advanced calculus. Ideally, each student’s preparation should include at least one term each of mathematical probability and mathematical statistics. Additional study in statistics and related mathematical areas, such as analysis and measure theory, is helpful. In the initial stages of graduate study, students should give high priority to acquiring the mathematical level required to satisfy their objectives.

As statistics is so intimately connected with computation, computation is an important part of almost all courses and research projects in the department. Preferably, students should have programming experience relevant for statistical computation and simulation.

Standardized Tests

GRE General: Optional GRE Subject: Optional

Theses & Dissertations

Theses & Dissertations for Statistics

See list of Statistics faculty

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Doctor of Philosophy in Statistics

Program description.

The Statistics PhD degree curriculum at The University of Texas at Dallas offers extensive coursework and intensive research experience in theory, methodology and applications of statistics. During their study, PhD students acquire the necessary skills to prepare them for careers in academia or in fields that require sophisticated data analysis skills.

The PhD program is designed to accommodate the needs and interests of the students. The student must arrange a course program with the guidance and approval of the graduate advisor. Adjustments can be made as the student’s interests develop and a specific dissertation topic is chosen.

Some of the broad research areas represented in the department include: probability theory, stochastic processes, statistical inference, asymptotic theory, statistical methodology, time series analysis, Bayesian analysis, robust multivariate statistical methods, nonparametric methods, nonparametric curve estimation, sequential analysis, biostatistics, statistical genetics, and bioinformatics.

Career Opportunities

Statisticians generally find employment in fields where there is a need to collect, analyze and interpret data — including pharmaceutical, banking and insurance industries, and government — and also in academia. The job of a statistician consistently appears near the top in the rankings of 200 jobs by CareerCast’s Jobs Rated Almanac based upon factors such as work environment, income, hiring outlook and stress.

For more information about careers in statistics, view the career page of American Statistical Association. UT Dallas PhD graduates are currently employed as statisticians, biostatisticians, quantitative analysts, managers, and so on, and also as faculty members in universities.

The  NSM Career Success Center  is an important resource for students pursuing STEM and healthcare careers. Career professionals are available to provide strategies for mastering job interviews, writing professional cover letters and resumes and connecting with campus recruiters, among other services.

Marketable Skills

Review the marketable skills for this academic program.

Application Deadlines and Requirements

The university  application deadlines apply with the exception that, for the upcoming Fall term, all application materials must be received by December 15 for first-round consideration of scholarships and fellowships. See the  Department of Mathematical Sciences graduate programs website  for additional information. 

Visit the  Apply Now  webpage to begin the application process. 

Contact Information

For more information, contact [email protected]

School of Natural Sciences and Mathematics The University of Texas at Dallas 800 W. Campbell Road Richardson, TX 75080-3021 Phone: 972-883-2416

nsm.utdallas.edu

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DEPARTMENT OF STATISTICS AND DATA SCIENCE

• For Current PhD Students

Required Courses for PhD

Required statistics and data science coursework:.

View requirements prior to 2021

The required Statistics and Data Science courses are:

• STAT 344 Statistical Computing
• STAT 350-0 Regression Analysis
• STAT 353-0 Advanced Regression
• STAT 415-0 Introduction to Machine Learning ( was STAT 435-0 Mathematical Foundations of Machine Learning in 2021-2022 )
• STAT 420-1 Introduction to Statistical Theory and Methodology 1
• STAT 420-2 Introduction to Statistical Theory and Methodology 2
• STAT 420-3 Introduction to Statistical Theory and Methodology 3
• STAT 457-0 Applied Bayesian Inference
• At least 4 electives (300- and 400-level graduate courses in Statistics), among which 2 must be 400 level. See STAT courses approved for the PhD coursework below. (STAT graduate level courses excluded for Statistics PhD students: STAT 301-1,2,3, STAT 303-1,2,3, STAT 320-1,2,3, STAT 330-1, and STAT 357) Independent Study registrations cannot be used to fulfill the coursework requirements. 

Additional Required Coursework:

In addition to the 12 courses listed above, PhD students must take:

• STAT 430-1 Probability for Statistical Inference 1 (offered in 2022-23)
• STAT 430-2 Probability for Statistical Inference 2 (offered in 2022-23)
• STAT 440 Stochastic Processes for Statistical Modeling and Inference (offered in 2022-23)

Approved STAT elective courses for PhD:

at least 2 elective courses must be 400 level

• STAT 302 Data Visualization
• STAT 328-0 Causal Inference
• STAT 348-0 Applied Multivariate Analysis
• STAT 351-0 Design Analysis of Experiments
• STAT 352-0 Nonparametric Statistical Methods
• STAT 354-0 Applied Time Series Modeling (currently would register for the STAT 359 section of this course)
• STAT 356-0 Hierarchical Linear Models
• STAT 359-0 Topics in Statistics
• STAT 365-0 Intro Analysis Financial Data
• STAT 439-0 Meta-Analysis
• STAT 455-0 Advanced Qualitative Data Analysis
• STAT 456-0 Generalized Linear Models
• STAT 461-0 Advanced Topics in Statistics
• STAT 465-0 Statistical Methods for Bioinformatics and Computational Biology

STAT 519 Requirement:

All PhD students are required to take STAT 519 Responsible Conduct of Research Training, typically in their second year.

Prior to 2021

The required Statistics courses are:

• STAT 350 Regression Analysis
• STAT 351 Design and Analysis of Experiments or IEMS 463 Statistical Analysis of Designed Experiments (DGS will specify)
• STAT 425 Sampling Theory and Applications
• 6 other 300 and 400 graduate level courses in Statistics to complete the 12 course requirement. Of these six, at least two should be 400 level courses. Independent Study registrations cannot be used to fulfill the coursework requirements. See STAT courses approved for the PhD coursework below.

In addition to the 12 courses listed above, PhD students must take either:

• MATH 450-1 Probability 1 and MATH 450-2 Probability 2
• MATH 450-1 Probability 1 and IEMS 460-1 Stochastic Processes 1 and IEMS 460-2 Stochastic Processes 2
• STAT 344-0 Statistical Computing
• STAT 370-0 Human Rights Statistics

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PhD Coursework

The schedule for PhD coursework in AY 2023-24 is as follows:

Real Analysis

Measure theory, Lebesgue integral, L p spaces, duality, representation theorems, Radon-Nikodym and Fubini theorem, differentiation of integrals, a few facts from harmonic analysis.

Advanced Linear Algebra

Rigorous treatment of vector and inner product spaces, LU factorization, QR factorization, spectral theorem and singular value decomposition, Jordan form, positive definite matrices, quadratic forms, partitioned matrices, norms and numerical issues, Hilbert spaces, compact operators, diagonalization of self-adjoint compact operators, Fredholm alternative.

Numerical Analysis

Machine arithmetic, linear systems, root finding, interpolation and quadrature, eigenvalue problems, ordinary differential equations.

Computational Mathematics

This course will survey key elements of computational mathematics with a particular emphasis on methods applicable to data. Course topics will include optimization, matrix analysis and approximation, graphs and networks, and linear and non-linear methods in dimension reduction and function approximation. An emphasis will be placed on computation in high dimensions and associated theory. Students who lack a working knowledge of a scripting language such as R or Python are welcome, but should talk to the instructor prior to taking the course.

Harmonic Analysis

The first part of the course concentrates on some fundamental results in Fourier analysis (Bochner’s theorem, Hardy-Littlewood maximal functions, Fefferman-Stein sharp functions, and the space of bounded mean oscillation) on Euclidean spaces. In the second part of this course, we are going to study singular integral operators through a few important example: Hilbert and Riesz transforms, the Szeg\{“}o projection operator on the Heisenberg group, and Cauchy integral on Lipschitz curves in the complex plane. Our goal is to explain some of the principal aspects of the great progress that has been made in the past thirty years or some toward understanding Calder\{‘}on-Zygmund operators.

Complex Analysis

Complex numbers. Analytic functions including exponential, logarithmic and trigonometric functions of a complex variable. Geometric and mapping properties of analytic functions. Contour integration, Cauchy’s theorem, the Cauchy integral formula. Power series representations. Residues and poles, with applications to the evaluation of integrals. Conformal mapping and applications as time permits.

Functional Analysis

Hilbert spaces, Banach spaces, convergence in topological vector spaces, dual spaces, Riesz representation theorem, Hahn-Banach theorem, open mapping theorem, closed graph theorem, principle of uniform boundedness, spectral theorem for (un)bounded operators, semigroups of linear operators, Fredholm operators and Fredholm index. Prerequisite: Real Analysis.

Probability

Topics include probability measures, independence and conditional probability, discrete and continuous random variables and their properties, joint distributions, moment generating functions, elements of Poisson processes, notions of convergence, Laws of Large Numbers, and the Central Limit Theorem. A working knowledge of multiple integrals and partial derivatives is essential for this course.

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10 facts about today’s college graduates

Having a bachelor’s degree remains an important advantage in many sectors of the U.S. labor market. College graduates generally out-earn those who have not attended college, and they are more likely to be employed in the first place. At the same time, many Americans say they cannot afford to get a four-year degree – or that they just don’t want to.

Here are key facts about American college graduates.

This Pew Research Center analysis about U.S. college graduates relies on data from sources including the Census Bureau, the Bureau of Labor Statistics, the National Center for Education Statistics, the National Student Clearinghouse and the Federal Reserve Bank, as well as surveys conducted by the Center.

Everyone who took the Pew Research Center surveys cited is a member of the Center’s American Trends Panel (ATP), an online survey panel that is recruited through national, random sampling of residential addresses. This way nearly all U.S. adults have a chance of selection. The survey is weighted to be representative of the U.S. adult population by gender, race, ethnicity, partisan affiliation, education and other categories. Read more about  the ATP’s methodology .

Nearly four-in-ten Americans ages 25 and older have a bachelor’s degree, a share that has grown over the last decade. As of 2021, 37.9% of adults in this age group held a bachelor’s degree, including 14.3% who also obtained a graduate or professional degree, according to data from the Census Bureau’s Current Population Survey. That share is up 7.5 percentage points from 30.4% in 2011.

An additional 10.5% had an associate degree in 2021. About four-in-ten Americans ages 25 and older had a high school diploma with no further education (25.3%) or completed some college but didn’t have a degree (14.9%).

In a reversal, women are now more likely than men to graduate from college, according to the Current Population Survey . In 2021, 39% of women ages 25 and older had a bachelor’s degree or more education, compared with 37% of men in the same age range. The gap in college completion is even wider among adults ages 25 to 34: 46% of women in this age group have at least a bachelor’s degree, compared with 36% of men.

In an October 2021 Pew Research Center survey of Americans without a degree, 34% of men said a major reason why they have not received a four-year college degree is that they just didn’t want to. Only one-in-four women said the same. Men were also more likely to say a major reason they didn’t have a four-year degree is that they didn’t need more education for the job or career they wanted (26% of men said this vs. 20% of women).

Women (44%) were more likely than men (39%) to say not being able to afford college was a major reason they don’t have a bachelor’s degree. Men and women were about equally likely to say a major impediment was needing to work to help support their family.

There are racial and ethnic differences in college graduation patterns, as well as in the reasons for not completing a degree. Among adults ages 25 and older, 61% of Asian Americans have a bachelor’s degree or more education, along with 42% of White adults, 28% of Black adults and 21% of Hispanic adults, according to 2021 Current Population Survey data. The share of bachelor’s degree holders in each group has increased since 2010. That year, 52% of Asian Americans had a four-year degree or more, compared with a third of White adults, 20% of Black adults and 14% of Hispanic adults.

The October 2021 Center survey found that among adults without a bachelor’s degree, Hispanic adults (52%) were more likely than those who are White (39%) or Black (41%) to say a major reason they didn’t graduate from a four-year college is that they couldn’t afford it. Hispanic and Black adults were more likely than their White counterparts to say needing to work to support their family was a major reason.

While a third of White adults said not wanting to go to school was a major reason they didn’t complete a four-year degree, smaller shares of Black (22%) and Hispanic (23%) adults said the same. White adults were also more likely to cite not needing more education for the job or career they wanted. (There weren’t enough Asian adults without a bachelor’s degree in the sample to analyze separately.)

Only 62% of students who start a degree or certificate program finish their program within six years, according to the most recent data from the  National Student Clearinghouse , a nonprofit verification and research organization that tracked first-time college students who enrolled in fall 2015 with the intent of pursuing a degree or certificate. The degree completion rate for this group was highest among students who started at four-year, private, nonprofit schools (78.3%), and lowest among those who started at two-year public institutions (42.2%).

Business is the most commonly held bachelor’s degree, followed by health professions.  According to the  National Center for Education Statistics , about a fifth (19%) of the roughly 2 million bachelor’s degrees conferred in 2019-20 were in business. Health professions and related programs were the second most-popular field, making up 12.6% of degrees conferred that year. Business has been the single most common major since 1980-81; before that, education led the way.

The  least  common bachelor’s degrees in 2019-20 were in military technologies and applied sciences (1,156 degrees conferred in 2019-20), library science (118), and precision production (39).

There is a growing earnings gap between young college graduates and their counterparts without degrees. In 2021, full-time workers ages 22 to 27 who held a bachelor’s degree, but no further education, made a median annual wage of $52,000, compared with $30,000 for full-time workers of the same age with a high school diploma and no degree, according to data from the Bureau of Labor Statistics. This gap has widened over time. Young bachelor’s degree holders earned a median annual wage of $48,481 in 1990, compared with $35,257 for full-time workers ages 22 to 27 with a high school diploma.

The unemployment rate is lower for college graduates than for workers without a bachelor’s degree, and that gap widened as a result of the coronavirus pandemic. In February 2020, just before the COVID-19 outbreak began in the U.S., only 1.9% of college graduates ages 25 and older were unemployed, compared with 3.1% of workers who completed some college but not a four-year degree, and 3.7% of workers with only a high school diploma. By June 2020, after the pandemic hit, 6.8% of college grads, 10.8% of workers with some college, and 12.2% of high school grads were unemployed.

By March 2022, the unemployment rate had nearly returned to pre-pandemic levels for college graduates (2%) while dropping to 3% among those with some college education but no four-year degree, and 4% among those with only a high school diploma.

Recent college graduates are more likely than graduates overall to be underemployed – that is, working in jobs that typically do not require a college degree, according to an analysis of Census Bureau and BLS data by the Federal Reserve Bank of New York . As of December 2021, 41% of college graduates ages 22 to 27 were underemployed, compared with 34% among all college graduates. The underemployment rates for recent college grads rose in 2020 as the COVID-19 outbreak strained the job market, but have since returned to pre-pandemic levels.

As of the end of 2021, only 34% of underemployed graduates ages 22 to 27 worked what the Fed defines as “good non-college jobs” – those paying at least $45,000 a year – down from around half in the 1990s. The share of underemployed graduates ages 22 to 27 in low-wage jobs – those earning less than $25,000 annually – rose from about 9% in 1990 to 11% last year.

When it comes to income and wealth accumulation, first-generation college graduates lag substantially behind those with college-educated parents, according to a May 2021 Pew Research Center analysis . Households headed by a first-generation college graduate – that is, someone who has completed at least a bachelor’s degree but does not have a parent with a college degree – had a median annual income of $99,600 in 2019, compared with $135,800 for households headed by those with at least one parent who graduated from college. The median wealth of households headed by first-generation college graduates ($152,000) also trailed that of households headed by someone with a parent who graduated from college ($244,500). The higher household income of the latter facilitates saving and wealth accumulation.

The gap also reflects differences in how individuals finance their education. Second-generation college graduates tend to come from  more affluent families , while first-generation college graduates are more likely to incur education debt than those with a college-educated parent.

Most Americans with college degrees see value in their experience. In the Center’s October 2021 survey , majorities of graduates said their college education was extremely or very useful when it came to helping them grow personally and intellectually (79%), opening doors to job opportunities (70%) and developing specific skills and knowledge that could be used in the workplace (65%).

Younger college graduates were less likely than older ones to see value in their college education. For example, only a third of college graduates younger than 50 said their college experience was extremely useful in helping them develop skills and knowledge that could be used in the workplace. Among college graduates ages 50 and older, 45% said this.

• Higher Education

About 1 in 4 U.S. teachers say their school went into a gun-related lockdown in the last school year

About half of americans say public k-12 education is going in the wrong direction, what public k-12 teachers want americans to know about teaching, what’s it like to be a teacher in america today, race and lgbtq issues in k-12 schools, most popular.

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