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Graduate Student Information

Section 4 Doctoral Degree Requirements

The PhD in Statistics And Applied Probability requires that all students pass three sequences of core courses, pass a qualifying exam and research project, and propose, write and defend a dissertation.

4.1 Core Courses

There are three core sequences of courses in the PhD program. All PhD students must pass these sequences with a grade of B or better. Each of these sequences consists of an A, B, and C part which are offered every year in Fall, Winter, and Spring quarters respectively.

4.1.1 Mathematical Statistics (207)

Prerequisites: This course assumes a good knowledge of basic statistical theory from courses like PSTAT 120ABC. The expectations are that students are proficient in mathematical reasoning like that used in real analysis (MATH 117) or other advanced math courses.

Course Description: Univariate and multivariate distribution theory, generating functions and order statistics. Estimation theory including minimum variance unbiased estimates, completeness, and sufficiency. Likelihood and Bayesian based methods of estimation. Hypothesis testing including likelihood ratio and score tests, uniformly most powerful tests, and unbiased tests. Confidence and credible intervals. Basic decision theory. Linear models. Asymptotic properties of inference.

4.1.2 Statistical Methods (220)

Prerequisites: We recommend a good working knowledge of regression and analysis of variance (PSTAT 126 and 122.) The course also requires familiarity with linear algebra (Math 108A.) Familiarity with statistical computing in R is recommended. PSTAT 127 Advanced Regression is also a course which offers good preparation for PSTAT 220B.

Course Description: Applied statistical techniques including graphical methods; estimation and inference; diagnostics; and model selection. R/SAS Computation.

  1. Regression; analysis of variance of fixed, random, and mixed effects models; analysis of covariance; and experimental design.

  2. Generalized linear models; log-linear models with application to categorical data; and nonlinear regression models.

  3. Multivariate analysis. Topics selected from factor analysis; canonical correlation analysis; classification and discrimination; clustering; and data mining.

4.1.3 Probability and Stochastic Processes (213)

Prerequisites: The minimum requirement is undergraduate probability training such as PSTAT 120A. Students are recommended to have some additional experience in probability topics. We offer an undergraduate Stochastic Processes course sequence (PSTAT 160A,B) which is good preparation for 213A. Students will also be expected to be proficient in mathematical reasoning like that used in real analysis (MATH 117) or other advanced math courses.

PSTAT 210 is required for 213B and 213C.

Course Content:

  1. Generating functions, discrete and continuous time Markov chains; random walks; branching processes; birth-death processes; Poisson processes, point processes.

  2. Convergence of random variables: different types of convergence; characteristic functions, continuity theorem, laws of large numbers, central limit theorem, large deviations, infinitely divisible and stable distributions, uniform integrability. Conditional expectation.

  3. Martingales, martingale convergence, stopping times, optional sampling, optional stopping theorems and applications, maximal inequalities. Brownian motion, introduction to diffusions.

PSTAT 210

PSTAT 210 Measure Theory for Probability is a math course designed to prepare our PhD students for PSTAT 213B. While this course is not strictly required for the degree, it is recommended unless you have previously taken a course in measure theory.

4.2 Preliminary Requirements

After completing the core sequences, PhD students are required to fulfill the two Preliminary Requirements. The first requirement is to pass a Qualifying Exam in either Statistics or Probability. The second requirement it to write a Research Report under the guidance of a faculty member.

MA Degree in Statistics

For MA/PhD students who were admitted to the Doctoral program but have not previously completed an MA degree, completion of the core courses and pass a qualifying exam will satisfy nearly all of the requirements for the MA degree in Statistics under the Mathematical Statistics option. You will only have to check that you have at least 42 units of courses completed.

Please notify the GPA when you are ready to file for the MA degree. It is highly recommended that you file for this degree when you become eligible because certain academic job titles in the department (eg. Teaching Associates) require that you have completed an MA.

4.3 Forming a Dissertation Committee

Each PhD student is responsible for finding a Research Advisor. This should be a tenure-track faculty member in the PSTAT department. If you want to work with a non-tenure-track faculty member or a faculty member from another department, then you are advised to find a co-Advisor in the department.

In consultation with this advisor, the student will form a Dissertation Committee. The main responsibility of this committee is to advise the student in their progress, and evaluate the Advancement to Candidacy Exam and Dissertation to determine that it has met the level of scholarship that is expected. The Research Advisor(s) is the chair of the committee, and the committee usually consists of two additional faculty from the PSTAT Department. Faculty from other departments at UCSB are eligible to serve on the committee as long as the majority of faculty on the committee are from PSTAT. See Graduate Division Committee Requirement for more policies regarding faculty eligible to serve on a committee and the forms that are needed to nominate or change a committee.

4.4 Advancing to Candidacy

Advancing to Candidacy is an important milestone in the career of a doctoral student. It indicates that course requirements have been completed, and the student is ready to turn their attention more completely towards the work of a researcher.

In order to be eligible to Advance to Candidacy, a doctoral student must have completed the required coursework. For most students, that is all 9 courses from the three core sequences PSTAT 207, PSTAT 213, and PSTAT 220 with a grade of B or better. There may be different required courses if you are pursuing an optional emphasis. You must also have passed two Area Requirements (qualifying exams) at the PhD level.

The Advancement Exam is a presentation on the topic you are planning for your Dissertation. This should include an extensive review of the existing scholarship in this field as well as a demonstration that you will likely be able to make a contribution to this field. As such, generally it is not required that you have made new discoveries or developed new methods at this stage. In most cases, it is enough to have some ideas or strategies and preliminary findings that indicate that this will be a fruitful avenue of exploration. The final word on whether your research is ready to Advance to Candidacy is up to your Dissertation Committee.

There are a few additional university rules that will be checked before you can advance:

  • Minimum 3.0 grade point average in all upper division and graduate classes completed since admission.
  • A transcript free of any “incomplete grades” or “no grades”.
  • Registration for three consecutive quarters, and registration during the quarter the student will advance.

It is your responsibility to meet with GPA to discuss your advancement so that you are sure that you have completed the requirements.

Advancement to Candidacy requires a fee that is to be paid at the Cashier’s Office before the student delivers the form to the Graduate Division. The fee can also be charged to the student’s BARC Account. Proof of payment is required on the Ph.D. Form II.

Students who wish to petition to add the Financial Mathematics and Statistics (FMS) optional Ph.D. emphasis require prior approval from the FMS committee before their oral examination is scheduled. Additional forms, in addition to Forms I and II need to be submitted to Graduate Division after paying an additional fee to formally add any optional Ph.D. emphasis (subject to emphasis committee approval). Please ask the Graduate Program Assistant and your Ph.D. committee chairperson for additional information.

4.5 Dissertation

The doctoral dissertation constitutes a major and essential part of earning the PhD degree. The dissertation contains original contributions to the field of statistics and applied probability that will expand the theory or methodology of the discipline. You are expected to work closely with your research advisor to jointly determine the aim and scope of your research work. The Department expectation is that you will work for two years after your advancement to candidacy to complete the dissertation.

Dissertation Defense

When you have completed your dissertation, it should be submitted to your Dissertation Committee for evaluation. After giving your committee sufficient time to review your dissertation (typically about two weeks), The final stage of this evaluation is your Dissertation Defense. A Dissertation Defense consists of a public presentation of your dissertation research.

The GPA can assist you in scheduling a room for your defense and posting announcements about the date and time of your presentation.

Immediately following this presentation, it is typical for you to meet with your committee to answer any question that they may have about the work. The Dissertation Committee is asked at that time to consider whether or not they approve that the dissertation is complete. The committee may present you with revisions that are necessary in order to get the dissertation approved. These revisions may be minor, or the committee may ask to see the revised dissertation before giving approval.

Filing Your Dissertation

Following your defense, you need to complete a final version of your dissertation which includes any revisions requested by your committee.

The Dissertation Committee will signify that they have approved the dissertation by signing the dissertation “approval page” (this is sometimes called the “signature page.”) This is the final approval that you need before filing to get your degree.

See the information on the Graduate Division Filing Best Practices site for updated information on the procedures for officially submitting your dissertation to the university.

There are important guidelines to how your dissertation should be formatted that you should consult early on.

Graduate Division also has a nice Filing Checklist you should use to make sure that you have completed all of the steps of the process.

4.6 First-Year Course Work

Students come to the PhD program in Statistics and Applied Probability with a great diversity of backgrounds and different aims of study. As a result, there is no one schedule expected in your first year.

Most students take at least one of the Core Sequences, and the sequence that is right for you depends on what direction you wish to pursue as well as how well prepared you are in the prerequisites for those sequences.

4.6.1 Transitioning into Statistics

For students who do not already have a degree in statistics, it may be that you should take prerequisite courses in your first year so that you will be better prepared to take the core sequences.

  • Fall Quarter
    • PSTAT 501 TA Training
    • PSTAT 126 Regression
    • PSTAT 122 Design of Experiments
    • MATH 117 Methods of Analysis
  • Winter Quarter
    • PSTAT 501 TA Training
    • PSTAT 120C Statistics
    • PSTAT 127 Advance Regression
    • PSTAT 160A Stochastic Processes
  • Spring Quarter
    • PSTAT 160B Stochastic Processes
    • PSTAT 274 Time Series Analysis

4.6.2 Applied Statistics

For students with an undergraduate degree in statistics that are hoping to pursue interdisciplinary work in statistical methodology, the 220 core sequence is definitely a good place to start. We also recommend taking the Statistical Consulting course because it is good experience and a key requirement to getting an MA in Applied Statistics along the way to the PhD.

  • Fall Quarter
    • PSTAT 501 TA Training
    • PSTAT 220A
    • PSTAT 122 Design of Experiments
  • Winter Quarter
    • PSTAT 501 TA Training
    • PSTAT 220B
    • PSTAT 231 Machine Learning
  • Spring Quarter
    • PSTAT 220C
    • PSTAT 230 Statistical Consulting

4.6.3 Data Science

Data Science is at the intersection between statistics, engineering, and science. Students will often want to begin with the 220 series as well as our 23x sequence of Data Science courses. There is also the opportunity to complete the MA track in Data Science as you are working towards the PhD.

  • Fall Quarter
    • PSTAT 501 TA Training
    • PSTAT 220A
    • PSTAT 234 Intro to Data Science
  • Winter Quarter
    • PSTAT 501 TA Training
    • PSTAT 220B
    • PSTAT 215A Bayesian Statistics
  • Spring Quarter
    • PSTAT 220C
    • PSTAT 231 Machine Learning
    • PSTAT 230 Statistical Consulting

4.6.4 Mathematical Statistics

Students who have additional mathematical training as well as a statistics background may be interested in pursuing more than one of the core sequences in the first year.

  • Fall Quarter
    • PSTAT 501 TA Training
    • PSTAT 220A
    • PSTAT 207A
  • Winter Quarter
    • PSTAT 501 TA Training
    • PSTAT 220B
    • PSTAT 207B
    • PSTAT 215A Bayesian Methods
  • Spring Quarter
    • PSTAT 220C
    • PSTAT 207C

4.7 Financial Mathematics Emphasis

For interested PhD students, there is the option to add an Emphasis in Financial Mathematics and Statistics (FMS). This emphasis requires extra coursework and includes less flexibility in your planning, but the fact that you completed the emphasis will be noted on your transcript when you graduate (the diploma will still be just “PhD in Statistics and Applied Probability.”)

4.7.1 Area Requirements (qualifying exams)

The emphasis requires that student complete the area requirements in Probability (213) and Mathematical Statistics (207).

4.7.2 Additional Core Courses

Students in FMS emphasis are also required to complete two additional sequences.

  • PSTAT 223ABC Financial Modeling is a 3-quarter sequence that is given Fall/Winter/Spring each year. PSTAT 223A in the Fall quarter covers stochastic Calculus and stochastic differential equations. PSTAT 223B in Winter quarter applies the stochastic calculus models to financial instruments and derivatives.Then in spring, PSTAT 223C expands on special topics in financial mathematics with different areas of study each year. Students in FMS will often re-take 223C in subsequent years through cross-registration with PSTAT 221 or 222 because a new topic is being offered.

  • MATH 201AB Real Analysis is a 2-quarter sequence in the Mathematics department covering measure theory and functional analysis.

As a consequence of these additional core sequences, students in the FMS are not required to complete PSTAT 220ABC.

4.7.3 Restricted Electives in FMS

In addition to the core sequences, students in the FMS emphasis also need to take 7 courses (28 units) from the list of restricted electives.

We can roughly divide these electives into broad categories:

  • Advanced Probability and Finance Courses
    • PSTAT 221 A,B,C Advanced Probability Theory
    • PSTAT 222 A,B,C Advanced Stochastic Processes
    • PSTAT 262 FM Special Topics in Financial Mathematics
  • Statistical Methodology
    • PSTAT 220 A, B, C Statistical Methods
    • PSTAT 274 Time Series
  • Mathematics
    • MATH 201 C Real Analysis
    • MATH 206 A, B, C, D Numerical Methods
    • MATH 228 A, B Functional Analysis
    • MATH 246 A, B, C Partial Differential Equations
  • Economics
    • ECON 210 A, B, C Microeconomics

4.7.4 Procedure for Adding the FMS Emphasis

Students should begin planning their coursework early on for the FMS emphasis. After you have completed all of the required courses, electives and passed the qualifying exams, then you may petition to add the emphasis.

  1. Complete this petition and have it signed by the FMS Graduate Advisor.
  2. Complete the change of degree petition and get it signed by the Graduate Advisor. The GPA can help you with getting this petition set up on DocuSign.

Most often these petitions are completed immediately before your advancement to candidacy.

4.7.5 Course Schedule for FMS Students

If you are thinking about pursuing the FMS emphasis, you should be aware that there are additional course requirements. Many of these courses are only offered in one quarter each year. As a result you need to plan carefully to meet all of the requirements.

A possible schedule for students who have already completed a Masters degree in mathematics or statistics might be.

  • First Year
    • Fall: PSTAT 207A, PSTAT 213A, PSTAT 210, PSTAT 501
    • Winter: PSTAT 207B, PSTAT 213B, PSTAT 501
    • Spring: PSTAT 207C, PSTAT 213C
  • Second Year
    • Fall: PSTAT 223A, MATH 201A
    • Winter: PSTAT 223B, MATH 201B
    • Spring: PSTAT 223C, MATH 201C
  • Third Year
    • Fall MATH 246A, PSTAT 220A
    • Winter MATH 215A, PSTAT 220B,
    • Spring PSTAT 220C, PSTAT 274

The bold course numbers are required, and while you do not have to take them all in two years, you should take them earlier because they are important pre-requisites for other courses. The italicized course numbers are electives, and you could swap in other electives to replace those.