Statistics

Faculty List

Associate Chair:  M. Evans (416-287-7274)

Probability and statistics have developed over a period of several hundred years as attempts to quantify uncertainty. With its origins in modeling games of chance, probability theory has become a sophisticated mathematical discipline with applications in such fields as demography, genetics and physics.

Statistics is concerned with the proper collection and analysis of data, both to reduce uncertainty and to provide for its assessment via probability. Applications range from pre-election polling to the design and analysis of experiments to determine the relative efficacies of different vaccines.

STAB22H3 and STAB27H3 serve as a non-technical introduction to statistics. These courses are designed for students from disciplines where statistical methods are applied. STAB52H3 is a mathematical treatment of probability. STAB57H3 is an introduction to the methods and theory of statistical inference. The C-level courses build on the introductory material to provide a deeper understanding of statistical methodology and of its practical implementation.

The Specialist Program in Statistics is eligible for inclusion in the Concurrent Teacher Education Program (CTEP). Please refer to the Concurrent Teacher Education section of this Calendar for further information.

Combining Statistics and Economics Programs
Students who wish to combine studies in statistics and economics should consult the Economics for Management section of this Calendar for information on the economics programs and restrictions on the order in which courses must be taken.

Service Learning and Outreach (Previously known as Science Engagement)
For experiential learning through community outreach and classroom in-reach, please see the Teaching and Learning section of this Calendar.

Statistics Programs

SPECIALIST PROGRAM IN MATHEMATICS (SCIENCE)

This program has a Statistics stream. For more information, see the Mathematics section of this Calendar.

SPECIALIST PROGRAM IN STATISTICS (SCIENCE)

Supervisor of Studies: S. Damouras Email: sdamouras@utsc.utoronto.ca (416-208-4794)

Program Objectives

This program provides training in the discipline of Statistics. Students are given a thorough grounding in the theory underlying statistical reasoning and learn the methodologies associated with current applications. A full set of courses on the theory and methodology of the discipline represent the core of the program. In addition students select one of two streams, each of which provides immediately useful, job-related skills. The program also prepares students for further study in Statistics and related fields.

The Quantitative Finance Stream focuses on teaching the computational, mathematical and statistical techniques associated with modern day finance. Students acquire a thorough understanding of the mathematical models that underlie financial modeling and the ability to implement these models in practical settings. This stream prepares students to work as quantitative analysts in the financial industry, and for further study in Quantitative Finance

The Statistical Machine Learning and Data Mining Stream focuses on applications of statistical theory and concepts to the discovery (or “learning”) of patterns in massive data sets.  This field is a recent development in statistics with wide applications in science and technology including computer vision, image understanding, natural language processing, medical diagnosis, and stock market analysis.  This stream prepares students for direct employment in industry and government, and further study in Statistical Machine Learning.

Program Requirements
To complete the program, a student must meet the course requirements described below. (One credit is equivalent to two courses.)

The first year requirements of the two streams are almost identical, except that the Quantitative Finance stream requires MGEA02H3/(ECMA04H3) while the Statistical Machine Learning and Data Mining stream requires CSCA67H; these courses need not be taken in the first year.  In the second year the two streams have considerable overlap.  This structure makes it relatively easy for students to switch between the two streams as their interests in Statistics become better defined.

Note: There are courses on the St. George campus that can be taken to satisfy some of the requirements of the program. STAB52H3, STAB57H3 and STAC67H3, however, must be taken at the University of Toronto Scarborough; no substitutes are permitted without permission of the program supervisor.

Core (7.5 credits)

1. Writing Requirement (0.5 credit) (*)
One of: ANTA01H3, ANTA02H3, (CLAA02H3), (CTLA19H3), CTLA01H3, ENGA10H3, ENGA11H3, ENGB06H3, ENGB07H3, ENGB08H3, ENGB09H3, ENGB17H3, ENGB19H3, ENGB50H3, ENGB51H3, GGRA02H3, GGRA03H3, GGRB05H3, (GGRB06H3), (HISA01H3), (HLTA01H3), ACMA01H3, (HUMA01H3), (HUMA11H3), (HUMA17H3), (LGGA99H3), LINA01H3, PHLA10H3, PHLA11H3, WSTA01H3.
(*) It is recommended that this requirement be satisfied by the end of the second year.

2. A-level courses (2.5 credits)
CSCA08H3 Introduction to Computer Programming
CSCA48H3 Introduction to Computer Science
MATA23H3 Linear Algebra I
One of:
     MATA31H3* Calculus I for Mathematical Sciences
     MATA30H3 Calculus I for Biological or Physical Sciences
One of:
     MATA37H3* Calculus II for Mathematical Sciences
     MATA36H3 Calculus II for Physical Sciences
(*) MATA31H3 and MATA37H3 are recommended; the latter requires the former.

3. B-level courses (2.5 credits)
MATB24H3 Linear Algebra II
MATB41H3 Techniques of the Calculus of Several Variables I
MATB61H3 Linear Programming and Optimization
STAB52H3 Introduction to Probability
STAB57H3 Introduction to Statistics

4. C-level courses (1.5 credits)
CSCC37H3 Introduction to Numerical Algorithms for Computational Mathematics
STAC62H3 Stochastic Processes
STAC67H3 Regression Analysis

5. D-level courses (0.5 credit)
STAD37H3 Multivariate Analysis

A. Quantitative Finance Stream
This stream requires a total of 26 courses (13.0 credits). In addition to the core requirements, 11 other courses (5.5 credits) must be taken satisfying all of the following requirements:

6. Additional A-level courses (0.5 credit)
MGEA02H3/(ECMA04H3) Introduction to Microeconomics: A Mathematical Approach

7. Additional B-level courses (2.0 credits)
ACTB40H3 Fundamentals of Investment and Credit
MATB42H3 Techniques of Calculus of Several Variables II
MATB44H3 Differential Equations I
STAB41H3 Financial Derivatives

8. Additional Upper Level courses (3.0 credits)
MATC46H3 Differential Equations II
STAC70H3 Statistics and Finance I
STAD57H3 Time Series Analysis
STAD70H3 Statistics and Finance II
Two of:
     APM462H1 Nonlinear Optimization
     CSCC11H3 Introduction to Machine Learning and Data Mining
     MATC37H3 Introduction to Real Analysis
     STAC51H3 Categorical Data Analysis
     STAC58H3 Statistical Inference
     STAC63H3 Probability Models
     STAD68H3 Advanced Machine Learning and Data Mining
     STAD94H3 Statistics Project

Note: Students enrolled in this stream should also consider taking complementary courses in economics and finance (e.g. MGEA06H3/(ECMA06H3), MGEB02H3/(ECMB02H3), MGEB06H3/(ECMB06H3), MGEC72H3/(ECMC49H3)), or a Minor in Economics for Management Studies.


B. Statistical Machine Learning and Data Mining Stream
This stream requires a total of 26 courses (13.0 credits). In addition to the core requirements, 11 other courses (5.5 credits) must be taken satisfying all of the following requirements:

6. Additional A-level courses (0.5 credit)
CSCA67H3 Discrete Mathematics for Computer Scientists

7. Additional B-level courses (1.0 credit)
Two of:
     CSCB07H3 Software Design
     CSCB20H3 Introduction to Databases and Web Applications
     CSCB36H3 Introduction to the Theory of Computation
     CSCB63H3 Design and Analysis of Data Structures

8. Additional Upper Level courses (4.0 credits)
CSCC11H3 Introduction to Machine Learning and Data Mining
STAC58H3 Statistical Inference
STAD68H3 Advanced Machine Learning and Data Mining
Five of: *
     Any C or D-level CSC, MAT or STA courses (excluding STAD29H3), three of which must be STA courses.
(*) Some of the courses on this list have prerequisites that are not included in this program; in choosing courses to satisfy this requirement, check the prerequisites carefully and plan accordingly.

SPECIALIST (CO-OPERATIVE) PROGRAM IN STATISTICS (SCIENCE)

Supervisor of Studies: S. Damouras (416-208-4794)  Email: sdamouras@utsc.utoronto.ca
Co-op Contact: askcoop@utsc.utoronto.ca

Program Objectives
This program combines the coursework of the Specialist Program in Statistics described above with paid work terms in public and private enterprises. It shares the goals and structure of the Specialist Program in Statistics, but complements study of the subject with considerable work experience.

Admission Requirements
Refer to the Program Admission requirements for the Specialist Program in Statistics described above and the Co-operative Programs section in this Calendar. Students entering this program must have a CGPA of at least 2.5.

Program Requirements
To remain in the program, a student must maintain a CGPA of 2.5 or higher throughout the program. To complete the program, a student must meet the work term and course requirements described below.

Work Term Requirements
Students must successfully complete three work terms, at most one of which can be during the summer. In addition, prior to their first work term, students must successfully complete the Arts & Science Co-op Work Term Preparation Activities. These include networking sessions, speaker panels and industry tours along with seminars covering resumes, cover letters, job interviews and work term expectations.

Course Requirements
The course requirements of the Co-operative Specialist Program in Statistics are identical to those of the Specialist Program in Statistics described above.

MAJOR PROGRAM IN STATISTICS (SCIENCE)

Supervisor of Studies: M. Samarakoon  Email: mahinda@utsc.utoronto.ca

Recommended Writing Course: Students are urged to take a course from the following list of courses by the end of their second year.
ANTA01H3, ANTA02H3, (CLAA02H3), (CTLA19H3), CTLA01H3, ENGA10H3, ENGA11H3, ENGB06H3, ENGB07H3, ENGB08H3, ENGB09H3, ENGB17H3, ENGB19H3, ENGB50H3, ENGB51H3, GGRA02H3, GGRA03H3, GGRB05H3, (GGRB06H3), (HISA01H3), (HLTA01H3), ACMA01H3, (HUMA01H3), (HUMA11H3), (HUMA17H3),  (LGGA99H3), LINA01H3, PHLA10H3, PHLA11H3, WSTA01H3.

Program Requirements
This program requires 8.0 full credits.

1. A-level courses
CSCA08H3 Introduction to Computer Programming 
MATA23H3 Linear Algebra I
One of:
     MATA30H3 Calculus I for Biological and Physical Sciences
     MATA31H3 Calculus I for Mathematical Sciences*
One of:
     MATA36H3 Calculus II for Physical Sciences
     MATA37H3 Calculus II for Mathematical Sciences*
*The sequence MATA31H3 and MATA37H3 is recommended. MATA31H3 is the pre-requisite for MATA37H3.

2. B-level courses
MATB24H3 Linear Algebra II
MATB41H3 Techniques of the Calculus of Several Variables I
MATB42H3 Techniques of the Calculus of Several Variables II
STAB52H3 An Introduction to Probability*
STAB57H3 An Introduction to Statistics*

Upper-level courses
STAC67H3 Regression Analysis*
Four of:
     any C- or D-level (or 300-400 on St. George) STA courses, except STAD29H3
Two of:
     ACTB40H3, or any C- or D-level (or 300-400 on St. George) CSC, MAT or STA courses
* STAB52H3, STAB57H3, STAC67H3 - These courses must be taken at UTSC. No substitutes are permitted without permission of the program supervisor.

MAJOR (CO-OPERATIVE) PROGRAM IN STATISTICS (SCIENCE)

Supervisor of Studies: M. Samarakoon (416-208-4748)  Email: mahinda@utsc.utoronto.ca
Co-op Contact: askcoop@utsc.utoronto.ca

Program Objectives
This program combines the coursework of the Major Program in Statistics described above with paid work terms in public and private enterprises. It shares the goals and structure of the Major Program in Statistics, but complements study of the subject with considerable work experience.

Admission Requirements
Refer to the Program Admission requirements for the Major Program in Statistics described above and the Co-operative Programs section in this Calendar. Students entering this program must have a CGPA of at least 2.5.

Program Requirements
To remain in the program, a student must maintain a CGPA of 2.5 or higher throughout the program. To complete the program, a student must meet the work term and course requirements described below.

Work Term Requirements
Students must successfully complete three work terms, at most one of which can be during the summer. In addition, prior to their first work term, students must successfully complete the Arts & Science Co-op Work Term Preparation Activities. These include networking sessions, speaker panels and industry tours along with seminars covering resumes, cover letters, job interviews and work term expectations.

Course Requirements
The course requirements of the Co-operative Major Program in Statistics are identical to those of the Major Program in Statistics described above.

MINOR PROGRAM IN STATISTICS (SCIENCE)

Supervisor of Studies: M. Samarakoon Email: mahinda@utsc.utoronto.ca

Program Requirements
This program requires 4.0 full credits.

First Year (2.0 credits)
CSCA08H3 Introduction to Computer Programming
MATA23H3 Linear Algebra I
[MATA30H3 Calculus I for Biological and Physical Sciences or MATA31H3 Calculus I for Mathematical Sciences] and
[MATA36H3 Calculus II for Physical Sciences or MATA37H3 Calculus II for Mathematical Sciences.] 
Notes:

1. The sequence MATA31H3 and MATA37H3 is recommended.
2. MATA31H3 is the pre-requisite for MATA37H3.

Second Year (1.0 credit)
STAB52H3 An Introduction to Probability
STAB57H3 An Introduction to Statistics

Third and Fourth Year (1.0 credit)
STAC67H3 Regression Analysis

In addition 0.5 credits must be chosen from any C- or D-level STA course but not STAD29H3.

MINOR PROGRAM IN APPLIED STATISTICS (SCIENCE)

Supervisor of Studies: K. Butler  Email: butler@utsc.utoronto.ca

Program Requirements
This program requires a total of 4.0 credits as follows:

One of (0.5 credit):
     CSCA08H3 Introduction to Computer Programming
     CSCA20H3 Computer Science for the Sciences
One of (0.5 credit):
     STAB22H3 Statistics I
     MGEB11H3/(ECMB11H3) Quantitative Methods in Economics I
     PSYB07H3 Data Analysis in Psychology
One of (0.5 credit):
     STAB27H3 Statistics II
     MGEB12H3/(ECMB12H3) Quantitative Methods in Economics II
     PSYC08H3 Advanced Data Analysis in Psychology

All of the following (1.5 credits):
STAC32H3 Applications of Statistical Methods
STAC50H3 Data Collection
STAD29H3 Statistics for Life and Social Scientists

Two (1.0 credit) of the following courses:
any ACT, CSC, MAT, STA course
[MGEA02H3/(ECMA04H3), MGEA06H3/(ECMA06H3), MGEB02H3/(ECMB02H3), MGEB06H3/(ECMB06H3), MGEC11H3/(ECMC11H3), MGED11H3/(ECMD10H3), MGED70H3/(ECMD70H3)]
GGRB02H3
HLTB15H3
[MGFB10H3/(MGTB09H3), MGFC30H3/(MGTC71H3), MGOC10H3/(MGTC74H3), MGMC01H3/(MGTD07H3), MGMD01H3/(MGTD30H3)]
POLB11H3

Statistics Courses

ACTB40H3    Fundamentals of Investment and Credit

This course is concerned with the concept of financial interest. Topics covered include: interest, discount and present values, as applied to determine prices and values of annuities, mortgages, bonds, equities, loan repayment schedules and consumer finance payments in general, yield rates on investments given the costs on investments.
Prerequisite: [MATA30H3 & one of MATA35H3, MATA36H3 or MATA37H3] or [(MATA27H3) & a cumulative GPA of 2.5 or higher] Note: Students enrolled in or planning to enrol in any of the B.B.A. programs are strongly urged not to take ACTB40H3 because ACTB40H3 is an exclusion for MGFB10H3/(MGTB09H3)/(MGTC03H3), a required course in the B.B.A. degree. Students in any of the B.B.A programs will thus be forced to complete MGFB10H3/(MGTB09H3)/(MGTC03H3), even if they have credit for ACTB40H3, but will only be permitted to count one of ACTB40H3 and MGFB10H3/(MGTB09H3)/(MGTC03H3) towards the 20 credits required to graduate from UofT Scarborough.
Exclusion: ACT240H, MGFB10H3/(MGTB09H3), (MGTC03H3).
Breadth Requirement: Quantitative Reasoning

STAB22H3    Statistics I

This course is a basic introduction to statistical reasoning and methodology, with a minimal amount of mathematics and calculation. The course covers descriptive statistics, populations, sampling, confidence intervals, tests of significance, correlation, regression and experimental design. A computer package is used for calculations.
Exclusion: ANTC35H3, MGEB11H3/(ECMB11H3), POLB11H3, PSYB07H3, (SOCB06H3), STAB52H3, STAB57H3, STA220H, STA250H
Breadth Requirement: Quantitative Reasoning

STAB27H3    Statistics II

This course follows STAB22H3, and gives an introduction to regression and analysis of variance techniques as they are used in practice. The emphasis is on the use of software to perform the calculations and the interpretation of output from the software. The course reviews statistical inference, then treats simple and multiple regression and the analysis of some standard experimental designs.
Prerequisite: STAB22H3
Exclusion: MGEB12H3/(ECMB12H3), STAB57H3, STA221H, STA250H
Breadth Requirement: Quantitative Reasoning

STAB41H3    Financial Derivatives

A study of the most important types of financial derivatives, including forwards, futures, swaps and options (European, American, exotic, etc). The course illustrates their properties and applications through examples, and introduces the theory of derivatives pricing with the use of the no-arbitrage principle and binomial tree models.
Prerequisite: ACTB40H3
Exclusion: MGFC30H3/(MGTC71H3)
Breadth Requirement: Quantitative Reasoning

STAB52H3    An Introduction to Probability

A mathematical treatment of probability. The topics covered include: the probability model, density and distribution functions, computer generation of random variables, conditional probability, expectation, sampling distributions, weak law of large numbers, central limit theorem, Monte Carlo methods, Markov chains, Poisson processes, simulation, applications. A computer package will be used.
Prerequisite: MATA33H3 or MATA36H3 or MATA37H3
Exclusion: STAB22H3, STA107H, STA257H
Breadth Requirement: Quantitative Reasoning

STAB57H3    An Introduction to Statistics

A mathematical treatment of the theory of statistics. The topics covered include: the statistical model, data collection, descriptive statistics, estimation, confidence intervals and P-values, likelihood inference methods, distribution-free methods, bookstrapping, Bayesian methods, relationship among variables, contingency tables, regression, ANOVA, logistic regression, applications. A computer package will be used.
Prerequisite: STAB52H3
Exclusion: STA261H
Breadth Requirement: Quantitative Reasoning

STAC32H3    Applications of Statistical Methods

A case-study based course, aimed at developing  students’ applied statistical skills beyond the basic techniques. Students will be required to write statistical reports.  Statistical software, such as SAS and R, will be taught and used for all statistical analyses.
Prerequisite: STAB27H3 or STAB57H3 or equivalents.
Breadth Requirement: Quantitative Reasoning

STAC50H3    Data Collection

The principles of proper collection of data for statistical analysis, and techniques to adjust statistical analyses when these principles cannot be implemented. Topics include: relationships among variables, causal relationships, confounding, random sampling, experimental designs, observational studies, experiments, causal inference, meta-analysis. Statistical analyses using SAS or R.
Prerequisite: STAB27H3 or STAB57H3 or equivalents.
Breadth Requirement: Quantitative Reasoning

STAC51H3    Categorical Data Analysis

Statistical models for categorical data. Contingency tables, generalized linear models, logistic regression, multinomial responses, logit models for nominal responses, log-linear models for two-way tables, three-way tables and higher dimensions, models for matched pairs, repeated categorical response data, correlated and clustered responses. Statistical analyses using SAS or R.
Prerequisite: STAB27H3 or STAB57H3 or equivalent.
Breadth Requirement: Quantitative Reasoning

STAC58H3    Statistical Inference

Principles of statistical reasoning and theories of statistical analysis. Topics include: statistical models, likelihood theory, repeated sampling theories of inference, prior elicitation, Bayesian theories of inference, decision theory, asymptotic theory, model checking, and checking for prior-data conflict. Advantages and disadvantages of the different theories.
Prerequisite: STAC62H3
Exclusion: STA352Y, STA422H
Breadth Requirement: Quantitative Reasoning

STAC62H3    Stochastic Processes

This course continues the development of probability theory begun in STAB52H3. Topics covered include finite dimensional distributions and the existence theorem, discrete time Markov chains, discrete time martingales, the multivariate normal distribution, Gaussian processes and Brownian motion.
Prerequisite: STAB52H3
Breadth Requirement: Quantitative Reasoning

STAC63H3    Probability Models

This course continues the development of probability theory begun in STAB52H3.  Probability models covered include branching processes, birth and death processes, renewal processes, Poisson processes, queuing theory, random walks and Brownian motion.
Prerequisite: STAB52H3
Breadth Requirement: Quantitative Reasoning

STAC67H3    Regression Analysis

Orthogonal projections. Univariate normal distribution theory. The linear model and its statistical analysis, residual analysis, influence analysis, collinearity analysis, model selection procedures. Analysis of designs. Random effects. Models for categorical data. Nonlinear models. Instruction in the use of SAS.
Prerequisite: STAB57H3
Exclusion: STA302H
Breadth Requirement: Quantitative Reasoning

STAC70H3    Statistics and Finance I

A mathematical treatment of option pricing. Building on Brownian motion, the course introduces stochastic integrals and Itô calculus, which are used to develop the Black-Scholes framework for option pricing. The theory is extended to pricing general derivatives and is illustrated through applications to risk management.
Prerequisite: [STAB41H3 or MGFC30H3/(MGTC71H3)] and STAC62H3
Corequisite: MATC46H3
Exclusion: APM466H, ACT460H
Breadth Requirement: Quantitative Reasoning

STAD29H3    Statistics for Life & Social Scientists

The course discusses many advanced statistical methods used in the life and social sciences. Emphasis is on learning how to become a critical interpreter of these methodologies while keeping mathematical requirements low. Topics covered include multiple regression, logistic regression, discriminant and cluster analysis, principal components and factor analysis.
Prerequisite: STAC32H3
Exclusion: All C-level/300-level and D-level/400-level STA courses or equivalents except STAC32H3, STAC50H3 and STA322H.
Breadth Requirement: Quantitative Reasoning

STAD37H3    Multivariate Analysis

Linear algebra for statistics. Multivariate distributions, the multivariate normal and some associated distribution theory. Multivariate regression analysis. Canonical correlation analysis. Principal components analysis. Factor analysis. Cluster and discriminant analysis. Multidimensional scaling. Instruction in the use of SAS.
Prerequisite: STAC67H3
Exclusion: STA437H, (STAC42H3)
Breadth Requirement: Quantitative Reasoning

STAD57H3    Time Series Analysis

An overview of methods and problems in the analysis of time series data. Topics covered include descriptive methods, filtering and smoothing time series, identification and estimation of times series models, forecasting, seasonal adjustment, spectral estimation and GARCH models for volatility.
Prerequisite: STAC62H3
Exclusion: STA457H, (STAC57H3)
Breadth Requirement: Quantitative Reasoning

STAD68H3    Advanced Machine Learning and Data Mining

Statistical aspects of supervised learning: regression, regularization methods, parametric and nonparametric classification methods, including Gaussian processes for regression and support vector machines for classification, model averaging, model selection, and mixture models for unsupervised learning. Some advanced methods will include Bayesian networks and graphical models.
Prerequisite: STAC58H3 and STAC67H3
Breadth Requirement: Quantitative Reasoning

STAD70H3    Statistics and Finance II

A survey of statistical techniques used in finance. Topics include mean-variance and multi-factor analysis, simulation methods for option pricing, Value-at-Risk and related risk-management methods, and statistical arbitrage. A computer package will be used to illustrate the techniques using real financial data.
Prerequisite: STAC70H3 and STAD37H3
Corequisite: STAD57H3
Breadth Requirement: Quantitative Reasoning

STAD92H3    Readings in Statistics

This course is offered by arrangement with a statistics faculty member. This course may be taken in any session and must be completed by the last day of classes in the session in which it is taken.
Prerequisite: Students must obtain consent from the Supervisor of Studies before registering for this course.
Breadth Requirement: Quantitative Reasoning

STAD93H3    Readings in Statistics

This course is offered by arrangement with a statistics faculty member. This course may be taken in any session and must be completed by the last day of classes in the session in which it is taken.
Prerequisite: Students must obtain consent from the Supervisor of Studies before registering for this course.
Breadth Requirement: Quantitative Reasoning

STAD94H3    Statistics Project

A significant project in any area of statistics. The project may be undertaken individually or in small groups. This course is offered by arrangement with a statistics faculty member. This course may be taken in any session and the project must be completed by the last day of classes in the session in which it is taken. Students must obtain consent from the Supervisor of Studies before registering for this course.

STAD95H3    Statistics Project

A significant project in any area of statistics. The project may be undertaken individually or in small groups. This course is offered by arrangement with a statistics faculty member. This course may be taken in any session and the project must be completed by the last day of classes in the session in which it is taken.
Prerequisite: Students must obtain consent from the Supervisor of Studies before registering for this course.
Breadth Requirement: Quantitative Reasoning