The PhD program in Statistics and Applied Probability at UC Santa Barbara prepares students to expand the boundaries of statistical theory and practice, equipping them with the skills to solve real-world problems. Graduates are trained for careers in academia, industry, and government, contributing to the forefront of new methods and technologies. The program provides rigorous mathematical training in statistics and probability, with applications in interdisciplinary fields such as finance, environmental science, computer science, and biomedical science.
Program Overview
Key Features
- Rigorous Training: Advanced coursework in statistical theory, probability, and applied methods.
- Research Opportunities: Dissertation topics span areas such as smoothing splines, spatial statistics, Bayesian inference, financial mathematics, and machine learning.
- Interdisciplinary Focus: Collaborations with fields like computer science, geography, economics, environmental science, and biostatistics.
Degree Requirements
Coursework
Students must pass the following required courses with a grade of B or better:
- Statistical Theory: PSTAT 207A, 207B, 207C (4 units each)
- Probability Theory & Stochastic Processes: PSTAT 213A, 213B, 213C (4 units each)
- Advanced Statistical Methods: PSTAT 220A, 220B, 220C (4 units each)
This is a total of 36 units. Students must also complete 36 units of graduate elective coursework in Statistics and Applied Probability. Students may enroll in PSTAT 596 Directed Reading and Research to fulfill up to 12 of these elective units.
Most PhD students complete their coursework within their first three years in the program.
Preliminary Requirements
PhD students must pass a Qualifying Exam in either Statistical Theory or Probability and Stochastic Processes. These exams are given each year in September.
PhD students must submit a Research Project that is approved by two faculty members. These projects could take a number of different forms. Some examples of the type of work that is expected
- A statistical analysis of a real data set requiring novel applications of statistical techniques,
- Development of an innovative computational tool,
- Review of a current area of research with a comparison of the competing approaches in the literature,
- New theory or argument on a question of current relevance.
Preliminary requirements (exams and projects) are typically completed in the first two years and must be completed before the beginning of the fourth year.
Choosing a Research Advisor
Students generally chose a research advisor in their second or third year. This is a faculty member in the department that you will work closely with to identify an area of mutual interest, develop a proposal for a dissertation project, complete that project while engaging the wider academic community through publications and presentations.
Advancement to Candidacy
Once PhD students have completed all the Required Courses and Preliminary Requirements and worked with a Research Advisor to investigate a possible area of study for the dissertation, they are eligible to Advance to Candidacy.
Advancing requires an oral presentation outlining the proposed dissertation topic as well as demonstrating that they have full knowledge of related work in that area and they have a reasonable chance to complete the proposed project.
PhD students are expected to advance at the end of their 3rd year.
Dissertation
The dissertation must contain an original contribution to the field of statistics and applied probability. Students will select a topic under the guidance of their advisor and doctoral committee.
The final step is a public Dissertation Defense presentation followed by filing the completed dissertation with the Graduate Division. For details, visit Filing Your Thesis/Dissertation.
Financial Mathematics and Statistics Emphasis
Financial Mathematics and Statistics (FMS) focuses on quantitative finance, risk management, and actuarial applications.
Students who are pursuing this emphasis have a different set of required courses
- Statistical Theory: PSTAT 207A, 207B, 207C (4 units each)
- Probability Theory & Stochastic Processes: PSTAT 213A, 213B, 213C (4 units each)
- Financial Modeling: PSTAT 223A, 223B, 223C (4 units each)
- Real Analysis: Math 201A, 201B
Elective courses must be chosen from the recommended elective lists.
Students interested in the FMS Emphasis are required to take the Probability Qualifying Exam.
An application to add the FMS emphasis should be submitted to the FMS Committee when all requirements have been completed and you have advanced to candidacy.
Students in the emphasis will work with researchers in the Center for Financial Mathematics and Actuarial Research on their dissertation work.
Time to Degree Expectations
The University has asked every department to establish normative times for advancement and degree completion. These are expectations based on students with the typical preparation.
The Department expects students to be able to complete the dissertation in 5 years after beginning the program.
Students should Advance to Candidacy at the end of their 3rd year.
However, the department acknowledges that students come to our program with diverse backgrounds, training, and strengths. We work with all students to establish an academic plan that works for them.