Statistical Sciences

Statistical Sciences: Introduction

​​​​​​​​​​​​​​​​​​​​​​​​Faculty Affilia​tion

Arts and Science​

Degree Programs

Financial Insurance

​M​​FI​​

Statistics

​MSc​
Fields:
Statistical Theory and Applications
Probability
​PhD​​​
Fields:
Statistical Theory and Applications
Probability
Actuarial Science and Mathematical Finance​

Overview

Statistical Sciences involves the study of random phenomena and encompasses a broad range of scientific, industrial, and social processes. As data become ubiquitous and easier to acquire, particularly on a massive scale, models for data are becoming increasingly complex. The past several decades have witnessed a vast impact of statistical methods on virtually every branch of knowledge and empirical investigation.

Please visit the departmental website for details about the fields offered, the research being conducted, and the courses. The department offers substantial computing facilities and operates a statistical consulting service for the University's research community. Programs of study may involve association with other departments such as Computer Science, Economics, Engineering, Mathematics, Public Health Sciences, and the Rotman School of Management. The department maintains an active seminar series and strongly encourages graduate student participation.

Contact and Address

MFI Program

Web: www.mfi.utoronto.ca
Email: info@mfi.utoronto.ca​
Telephone: 416-978-5136
Fax: 416-978-5133

Department of Statistical Sciences
Sidney Smith Hall
University of Toronto
Room 6018, 100 St. George Street
Toronto, Ontario M5S 3G3
Canada

MSc and PhD Programs

Web: www.utstat.utoronto.ca
Email: grad-info@utstat.utoronto.ca
Telephone: (416) 978-5136
Fax: (416) 978-5133

Department of Statistical Sciences
University of Toronto
Sidney Smith Hall
Room 6022, 100 St. George Street
Toronto, Ontario M5S 3G3
Canada

Statistical Sciences: Graduate Faculty

Full Members

Badescu, Andrei - BSc, MSc, DPhil
Brenner, David - BSc, MSc, PhD
Briollais, Laurent - BSc, MSc, PhD
Broverman, Samuel - BSc, MSc, PhD
Brown, Patrick - BA, MSc, PhD
Brunner, Lawrence - BA, MA, PhD, DPhil
Craiu, Virgil Radu - BSc, MSc, PhD (Associate Chair, Graduate Studies)
Duvenaud, David - PhD
Escobar, Michael - BS, PhD
Evans, Michael - BSc, MSc, PhD
Feuerverger, Andrey - BSc, PhD
Fortin, Marie-Josee - MSc, PhD
Goldenberg, Anna - PhD
Grosse, Roger - PhD
Jaimungal, Sebastian - BSc, MSc, PhD
Knight, Keith - BSc, MS, PhD
Kong, Dehan - BS, MS, PhD
Lin, Xiaodong - BSc, MSc, MMath, PhD
Lou, Wen-Yi Wendy - DPhil
Quastel, Jeremy - BSc, MS, PhD
Reid, Nancy - BM, MSc, PhD, FRSC
Rosenthal, Jeffrey - BSc, AM, PhD, FRSC
Stafford, James - BS, MS, PhD (Chair and Graduate Chair)
Sun, Lei - BS, PhD
Virag, Balint - BA, MA, PhD
Volgushev, Stanislav - MA, PhD
Yao, Fang - BSc, MSc, DPhil
Zhou, Zhou - MSc, DPhil

Members Emeriti

Andrews, David - BSc, MSc, PhD
Corey, Paul - BSc, MA, PhD
Fraser, Donald AS - BA, MA, PhD, FRSC
Guttman, Irwin - BSc, MA, PhD
Srivastava, Muni - MSc, PhD

Associate Members

Gibbs, Alison - BSc, MSc, PhD
Rubisov, Dmitri - ME, PhD
Taback, Nathan - BSc, MSc, PhD
White, Bethany - DSc, DSc, DSc, DSc
Willmot, Gordon - BMath, MMath, PhD

Statistical Sciences: Financial Insurance MFI

Master of Financial Insurance

Program Description

The MFI is a full-time professional program based on three pillars: statistical methods, financial mathematics, and insurance modelling. This program is appropriate for students with backgrounds in statistics, actuarial science, economics, and mathematics. Students with a quantitative background (such as physics and engineering) and sufficient statistical training are also encouraged to apply.

 

Minimum Admission Requirements

  • Applicants are admitted under the General Regulations of the School of Graduate Studies. Applicants must also satisfy the Department of Statistical Sciences' additional admission requirements stated below.

  • An appropriate bachelor’s degree from a recognized university in a related field such as statistics, mathematics, finance, and actuarial science, or any discipline where there is a significant quantitative component. Studies must include significant exposure to statistics, mathematics, finance, and actuarial science, including coursework in advanced calculus, computational methods, linear algebra, probability, and statistics.

  • An average grade equivalent to at least a University of Toronto B+ in the final year or over senior courses; applicants who meet the SGS grade minimum of mid-B and demonstrate exceptional ability through appropriate workplace experience will be considered.

  • Three letters of reference.

  • A curriculum vitae detailing the student’s educational background, professional experience, and skills.

  • Applicants whose primary language is not English and who graduated from a university where the language of instruction and examination was not English must demonstrate proficiency in English using one of the official methods outlined in the SGS Calendar.

  • Selected applicants may be required to attend an interview.

Admission to the program is competitive, and achievement of the minimum admission standards does not guarantee admission into the program.

 

Program Requirements

  • ​Students must successfully complete 5.5 full-course equivalents (FCEs) as follows:

    • ​Nine required half courses (4.5 FCEs).

    • STA 2560Y Industrial Internship, a 3.5-month summer internship (1.0 FCE). Students must submit a project proposal to the program director and select an advisor by April 15. Students will propose a placement site to be approved by the department. The department will provide approval of the proposal by May 15. An interim report is required by July 7. Students must prepare a final written report and deliver an oral presentation on the internship project at the conclusion of the internship.

​​Required Courses
Fall Session​
​MMF 2021H
Numerical M​ethods for Finance​
​STA 2503H
Applied Probability for Mathematical Finance​
​STA 2530H
​Applied Time-Series Analysis
​STA 2535H
Life Insurance Mathematics​
​STA 2550H+
Financial Insurance Seminar Series (Credit/No Credit)​
Winter Session
​ECO 2506​H
Economics of Risk Management​
​STA 2540H
Insurance Risk Management​
​STA 2551H
​Financial Insurance Case Studies
​STA 2536H
Non-life Insurance Mathematics​
​STA 2550H+
Financial Insurance Seminar Series (Credit/No Credit)​
Summer Session
STA 2560Y
​Industrial Internship

+ Extended course. For academic reasons, coursework is extended into session following academic session in which course is offered.

 

Program Length

3 sessions full-time (typical registration sequence: F/W/S)

Time Limit

3 years full-time

Statistical Sciences: Statistics MSc

Master of Science​​

Program Description

Students in the MSc program can conduct research in the fields of (a) Statistical Theory and Applications or (b) Probability. The program offers numerous courses in theoretical and applied aspects of Statistical Sciences, which prepare students for pursuing a PhD program or directly entering the data science workforce.

The MSc program can be taken on a full-time or part-time basis. Program requirements are the same for the full-time and part-time options.

 

Fields:
Statistical Theory and Applications​
Probability

Minimum Admission Requirements

  • Admission to the MSc program is competitive, and applicants are admitted under the General Regulations of the School of Graduate Studies. Admission requirements for the Statistical Theory and Applications field and the Probability field are identical. Successful applicants have:

    • ​​​An appropriate bachelor's degree from a recognized university in a related field such as statistics, actuarial science, mathematics, economics, engineering, or any discipline where there is a significant quantitative component. Studies must include significant exposure to statistics, computer science, and mathematics, including coursework in advanced calculus, computational methods, linear algebra, probability, and statistics.

    • An average grade equivalent to at least a University of Toronto mid-B in the final year or over senior courses.

    • Three letters of reference.

    • A curriculum vitae.

  • Applicants whose primary language is not English and who graduated from a university where the language of instruction and examination was not English must demonstrate proficiency in English. See General Regulations section 4.3 for requirements.

Program Requirements

  • Both the Statistical Theory and Applications field and the Probability field have the same program requirements. All programs must be approved by the Associate Chair for Graduate Studies.

  • Students must complete a total of 4.0 full-course equivalents (FCEs), of which 2.0 must be chosen from the list below:

    • ​​STA 2101H Methods of Applied Statistics I.

    • STA 2201H Methods of Applied Statistics II

    • STA 2111H Probability Theory I

    • STA 2211H Probability Theory II

    • STA 2112H Mathematical Statistics I

    • STA 2212H Mathematical Statistics II.

  • The remaining 2.0 FCEs may be selected from:

    • ​​​any Department of Statistical Sciences 2000-level course or higher

    • any 1000-level course or higher in another graduate unit at the University of Toronto with sufficient statistical, computational, probabilistic, or mathematical content

    • one 0.5 FCE as a reading course

    • one 0.5 FCE as a research project

    • a maximum of 1.0 FCE from any STA 4500-level modular course (each are 0.25 FCE)​.

  • All programs must be approved by the Associate Chair for Graduate Studies. Students must meet with the Associate Chair to ensure that their program meets the requirements and is of sufficient depth.

  • Part-time students are limited to taking 1.0 FCE during each session. In exceptional cases, the Associate Chair for Graduate Studies may approve 1.5 FCEs in a given session.

Program Length

3 sessions full-time (typical registration sequence: F/W/S);
6 sessions part-time

Time Limit

3 years full-time;
6 years part-time

Statistical Sciences: Statistics PhD

​​Doctor of Philosophy​

Program Description

Students in the PhD program can conduct research in the fields of (a) Statistical Theory and Applications or (b) Probability or (c) Actuarial Science and Mathematical Finance. The research conducted in the department is vast and covers a diverse set of areas in theoretical and applied aspects of Statistical Sciences. Students have the opportunity to work in multidisciplinary areas and team up with researchers in, for example, Biostatistics, Computer Science, Economics, Engineering, and the Rotman School of Management. The main purpose of the program is to prepare students for pursuing advanced research both in academia and in research institutes.

Applicants may enter the PhD program via one of two routes: 1) following completion of an appropriate master’s degree or 2) direct entry after completing an appropriate bachelor’s degree.

 

Fields:
Statistical Theory and Applications
Probability

PhD Program

Minimum Admission Requirements

  • Admission to the PhD program is competitive, and applicants are admitted under the General Regulations of the School of Graduate Studies.

  • Applicants may be accepted with a master's degree in statistics from a recognized university with at least a B+ average. Applicants with degrees in biostatistics, computer science, economics, engineering, mathematics, physics, or any discipline where there is a significant quantitative component will be also be considered.

  • Three letters of recommendation.

  • A curriculum vitae.

  • A letter of intent or personal statement outlining goals for graduate studies.

  • Applicants whose primary language is not English and who graduated from a university where the language of instruction and examination was not English must demonstrate proficiency in English. See General Regulations section 4.3 for requirements.

Program Requirements

Course Requirements
  • During Year 1, students are required to complete the following 3.0 full-course equivalents (FCEs):

    • ​​​STA 2111H Probability Theory I

    • STA 2211H Probability Theory II

    • STA 2101H Methods of Applied Statistics I

    • STA 2201H Methods of Applied Statistics II

    • STA 3000Y Advanced Theory of Statistics.

Comprehensive Examination Requirements
  • At the end of Year 1, students must attempt the following comprehensive examinations:

    • ​​​​Probability

    • Theoretical Statistics

    • Applied Statistics.

      All three examinations must be passed by the end of Year 2.

Thesis Requirements

Conducting original research is the most important part of doctoral work. The thesis document must constitute significant and original contribution to the field. Students will have yearly meetings with a committee of no less than three faculty members to assess their progress. The completed thesis must be presented and defended within the Department of Statistical Sciences in addition to being presented and defended at the School of Graduate Studies.

 

Residency Requirements

Students must also satisfy a two-year residency requirement, whereby students must be on campus full-time and consequently in geographical proximity to be able to participate fully in the University activities associated with the program.

 

Program Length

4 years

Time Limit

6 years

 

PhD Program (Direct-Entry)

Minimum Admission Requirements

  • Admission to the PhD program is competitive, and applicants are admitted under the General Regulations of the School of Graduate Studies.

  • Applicants may be accepted via direct entry with a bachelor's degree in statistics from a recognized university with at least an A- average. The department also encourages applicants from biostatistics, computer science, economics, engineering, mathematics, physics, or any discipline where there is a significant quantitative component.

  • Three letters of recommendation.

  • A curriculum vitae.

  • A letter of intent or personal statement outlining goals for graduate studies.

  • Applicants whose primary language is not English and who graduated from a university where the language of instruction and examination was not English must demonstrate proficiency in English. See General Regulations section 4.3 for requirements.

Program Requirements

Course Requirements
  • During Year 1, students are required to complete the following 3.0 full-course equivalents (FCEs):

    • ​​​STA 2111H Probability Theory I

    • STA 2211H Probability Theory II

    • STA 2101H Methods of Applied Statistics I

    • STA 2201H Methods of Applied Statistics II

    • STA 3000Y Advanced Theory of Statistics.

  • Students must complete an additional 2.0 FCEs at the graduate level. The additional courses must be approved by the Associate Chair of Graduate Studies.

Comprehensive Examination Requirements
  • At the end of Year 1, students must attempt the following comprehensive examinations:

    • ​​​​Probability

    • Theoretical Statistics

    • Applied Statistics.

      All three examinations must be passed by the end of Year 2.

Thesis Requirements

Conducting original research is the most important part of doctoral work. The thesis document must constitute significant and original contribution to the field. Students will have yearly meetings with a committee of no less than three faculty members to assess their progress. The completed thesis must be presented and defended within the Department of Statistical Sciences in addition to being presented and defended at the School of Graduate Studies.

 

Residency Requirements

Students must also satisfy a three-year residency requirement, whereby students must be on campus full-time and consequently in geographical proximity to be able to participate fully in the University activities associated with the program.

 

Program Length

5 years

Time Limit

7 years

 

Field: Actuarial Science and Mathematical Finance

PhD Program

Minimum Admission Requirements

  • Admission to the PhD program is competitive, and applicants are admitted under the General Regulations of the School of Graduate Studies.

  • Applicants may be accepted with a master's degree in statistics from a recognized university with at least a B+ average. Applicants with degrees in biostatistics, computer science, economics, engineering, mathematics, physics, or any discipline where there is a significant quantitative component will be also be considered.

  • Three letters of recommendation.

  • A curriculum vitae.

  • A letter of intent or personal statement outlining goals for graduate studies.

  • Applicants whose primary language is not English and who graduated from a university where the language of instruction and examination was not English must demonstrate proficiency in English. See General Regulations section 4.3 for requirements.

Program Requirements

Course Requirements
  • During Year 1, students must complete the following 3.0 full-course equivalents (FCEs):

    1. All of:

      • STA 2111H Probability Theory I,

      • STA 2211H Probability Theory II, and

      • STA 2503H Applied Probability for Mathematical Finance

    2. One of:

      • STA 4246H Research Topics in Mathematical Finance or

      • STA 2501H Mathematical Risk Theory

    3. Either:

      • STA 3000Y Advanced Theory of Statistics or

      • STA 2101H Methods of Applied Statistics I and

      • STA 2201H Methods of Applied Statistics II.

Comprehensive Examination Requirements
  • ​​​​At the end of Year 1, students must attempt the following comprehensive examinations:

    • Probability

    • Actuarial Science and Mathematical Finance

    • Theoretical Statistics or Applied Statistics.

      All three examinations must be passed by the end of Year 2.

Thesis Requirements

Conducting original research is the most important part of doctoral work. The thesis document must constitute significant and original contribution to the field. Students will have yearly meetings with a committee of no less than three faculty members to assess their progress. The completed thesis must be presented and defended within the Department of Statistical Sciences in addition to being presented and defended at the School of Graduate Studies.

 

Residency Requirements

Students must also satisfy a three-year residency requirement, whereby students must be on campus full-time and consequently in geographical proximity to be able to participate fully in the University activities associated with the program.

 

Program Length

5 years

Time Limit

7 years

Statistical Sciences: Statistics MSc, PhD Courses

The department offers a selection of courses each year from the following list with the possibility of additions. The core courses will be offered each year. Visit the department's website for courses offered in the current academic year.

​STA 1001​H
​Applied Regression​ Analysis
​STA 1002H
​Methods of Data Analysis
​STA 1003H
Sample Survey Theory and its Application​
​STA 1007H
​Statistics for Life and Social Scientists
​STA 1008H
​Applications of Statistics
​STA 2004H
​Design of Experiments
​STA 2005H
​Applied Multivariate Analysis
​STA 2006H
​Applied Stochastic Processes
​STA 2047H
​Stochastic Calculus
​STA 2080H
​Fundamentals of Statistical Genetics
​STA 2100H
​Mathematical Methods for Statistics
​STA 2101H
​Methods of Applied Statistics I
​STA 2102H
​Computational Techniques in Statistics
​STA 2104H
​Statistical Methods for Machine Learning and Data Mining
​STA 2105H
​Nonparametric Methods of Statistics
​STA 2111H
​Probability Theory I
​STA 2112H
​Mathematical Statistics I
​STA 2162H
​Statistical Inference I
​STA 2201H
​Methods of Applied Statistics II
​STA 2202H
​Time Series Analysis
​STA 2209H
​Lifetime Date Modelling and Analysis
​STA 2211H
​Probability Theory II
​STA 2212H
​Mathematical Statistics II
​STA 2342H
​Multivariate Analysis I
​STA 2453H
​Statistical Consulting
​STA 2500H
Loss Models
​STA 2501H
​Mathematical Risk Theory
​STA 2502H
​Stochastic Models in Investments
​STA 2503H
​Applied Probability for Mathematical Finance
​STA 2505H
​Credibility Theory and Simulation Methods
​STA 2542H
​Linear Models
​STA 2530H
​Applied Time-Series Analysis
​STA 2535H
​Life Insurance Mathematics
​STA 2536H
​Non-life Insurance Mathematics
​STA 2540H
​Insurance Risk Management​
​STA 2550H+
​Financial Insurance Seminar Series (Credit/No Credit)
​STA 2551H
​Financial Insurance Case Studies
​STA 2560Y
​Industrial Internship
​STA 3000Y
​Advanced Theory of Statistics
​STA 3431H
​Monte Carlo Methods
​STA 4000H, ​Y​
​Supervised Reading Project I
​STA 4001H, Y
​Supervised Reading Project II
​​STA 4002H
Supervised Reading Project for an Advanced Special Topic
​STA 4246H
​Research Topics in Mathematical Finance
​STA 4247H
​Point Processes, Noise, and Stochastic Analysis
​STA 4273H
​Research Topics in Statistical Machine Learning
​STA 4315H
​Computational Methods in Statistical Genetics
​STA 4364H
​Conditional Inference: Sample Space Analysis
​STA 4412H
​Topics in Theoretical Statistics Modular Courses

Note: The following modular courses are each worth 0.25 full-course equivalents (FCEs).

​STA 4500H
​Statistical Dependence: Copula Mo​dels and Beyond
​STA 4501H
Functional Data Analysis and Related Topics​
​STA 4502H
​Monte Carlo Estimation
​STA 4503H
​Advanced Monte Carlo Methods and Applications
​STA 4504H
​An Introduction to Bootstrap Methods
​STA 4505H
​Applied Stochastic Control: High Frequency and Algorithmic Trading
​STA 4506H
​Non-stationary Time Series Analysis
​STA 4507H
Extreme Value Theory and Applications​
​STA 4508H
​Topics in Likelihood Inference
​STA 4509H
​Insurance Risk Models I
​STA 4510H
​Insurance Risk Models II
​STA 4511H
​Statistical Issues in Number Theory
​STA 4512H
​Logical Foundations of Statistical Inference
​STA 4513H​
​Statistical Models of Networks, Graphs, and Other Relational Structures
​STA 4514​H
​Modelling and Analysis of Spatially Correlated Data
STA 4515H Multiple Hypothesis Testing and its Applications
STA 4516H
Topics in Probabilistic Programming

+ Extended course. For academic reasons, coursework is extended into session following academic session in which course is offered.