Current & Upcoming Timetable

(also offered as undergraduate course STA437H1)

Practical techniques for the analysis of multivariate data; fundamental methods of data reduction with an introduction to underlying distribution theory; basic estimation and hypothesis testing for multivariate means and variances; regression coefficients; principal components and the partial multiple and canonical cor relations; multivariate analysis of variance;  classification and the linear discriminant function. The use of R software should be  expected.

The topics will vary year to year and give students the flexibility to examine a diverse range of subjects relevant to applied statistics and data science. This special topics course is repeatable for credit if taken with a different individual topic.

September 2022: "Structural Equation Models".

The classical structural equation models are extensions of multiple regression. They are based on systems of linear regression-like equations, usually with latent as well as observed variables. Examples include regression with measurement error, confirmatory factor analysis and path analysis, as well as many econometric models. This course will focus on issues such as original and surrogate models, robustness and parameter identifiability. The computer algebra software SageMath will be used to make certain calculations less burdensome. For data analysis, we will use R's lavaan package. Knowledge of linear models and maximum likelihood at the undergraduate level is required, but prior familiarity with SageMath and lavaan will not be assumed. Assessment will be based on in-class quizzes and take-home data analysis assignments.

Prerequisite:

• permission by the instructor

This course will focus on principles and methods of applied statistical science. It is designed for MSc and PhD students in Statistics, and is required for the Applied Paper of the PhD comprehensive exams.  The topics covered include: planning of studies, review of linear models, analysis of random and mixed effects models, model building and model selection, theory and methods for generalized linear models, and an introduction to nonparametric regression. Additional topics will be introduced as needed in the context of case studies in data analysis.

STA 2111H is a course designed for Master’s and Ph.D. level students in statistics, mathematics, and other departments, who are interested in a rigorous, mathematical treatment of probability theory using measure theory. Specific topics to be covered include: probability measures, the extension theorem, random variables, distributions, expectations, laws of large numbers, Markov chains.

Students should have a strong undergraduate background in Real Analysis, including calculus, sequences and series, elementary set theory, and epsilon-delta proofs. Some previous exposure to undergraduate-level probability theory is also recommended.

This course is designed for graduate students in Statistics and Biostatistics.

Review of probability theory, distribution theory for normal samples, convergence of random variables, statistical models, sufficiency and ancillarity, statistical functionals,influence curves, maximum likelihood estimation, computational methods.

(also offered as undergraduate course STA457H1)

An overview of methods and problems in the analysis of time series data. Topics include: descriptive methods, filtering and adjustment, spectral estimation, bivariate time series models.

The course will cover the following topics:

• Theory of stationary processes, linear processes
• Elements of inference in time domain with applications
• Spectral representation of stationary processes
• Elements of inference in frequency domain with applications
• Theory of prediction (forecasting) with applications > ARMA processes, inference and forecasting
• Non-stationarity and seasonality, ARIMA and SARIMA processes

Further topics, time permitting: multivariate models; GARCH models; state-space models

This course is designed to provide graduate students with experience in statistical consulting. Students are active participants in research projects brought to the Statistical Consulting Service (SCS) of the Department of Statistics. The course is offered over the two sessions, fall (September-December) and winter (January-April). The overall workload is approximately equivalent to a half graduate course and students receive a half credit.

Students are not expected to have had any experience as consultants. The purpose of the course is to provide this experience so that graduates will be better able to function in such an environment when they have completed the course. The course also provides students with the opportunity to become familiar with statistical software packages such as The SAS System. There is supervision and assistance to novice consultants.

Content: There is some classroom instruction at the start of the term, an d meetings occasionally are called to discuss special topics and for students to compare experiences. Students serve as apprentice statisticians and work under the guidance of the instructor and the SCS Coordinator on individual projects. Projects are assigned to students as they come in to the SCS. There are periods of inactivity when there are no projects and other times are very busy. The pattern of work is more like that associated with a business or working environment than a traditional course. While some consideration is taken of other academic demands on students, those enrolling must be aware that work on projects may require precedence at times.

Evaluation: Students will be graded on the quality of their work as stati stical consultants. This involves the ability to do work in a timely fashion, the quality of advice provided and the quality of the presentation of advice and written work to clients.

Recommended Preparation: Students should have taken some applied sta tistics courses such as an undergraduate regression course. Also undergraduate courses in applied statistics, sample survey, design of experiments and time series analysis are recommended but these are not required. Also taking some of the other 2000 level applied statistics courses is recommended as this course will serve as an excellent opportunity to put the content of these courses to work.

Parametric distributions and transformations, insurance coverage modifications, limits and deductibles, models for claim frequency and severity, models for aggregate claims,stop-loss insurance, risk measures.

Prerequisite: Consult the instructor concerning necessary background for this course.

(also offered as undergraduate course ACT460H1)

This course is an introduction to the stochastic models used in Finance and Actuarial Science. Students will be exposed to the basics of stochastic calculus, particularly focusing on Brownian motions and simple stochastic differential equations. The role that martingales play in the pricing of derivative instruments will be investigated. Some exotic equity derivative products will be explored together with stochastic models for interest rates.

Recommended Preparation:

• Knowledge of undergraduate probability theory is necessary.
• Knowledge of basic financial modeling (e.g., binomial trees and log-normal distributions) is useful, but not completely necessary.

This course features studies in derivative pricing theory and focuses on financial mathematics and its applications to various derivative products. A working knowledge of probability theory, stochastic calculus (see e.g., STA 2502), knowledge of ordinary and partial differential equations and familiarity with the basic financial instruments is assumed.

The tentative topics covered in this course include, but is not limited to:

• no-arbitrage and the fundamental theorem of asset pricing,
• binomial pricing models;
• continuous time limits;
• the Black-Scholes model;
• the Greeks and hedging;
• European, American, Asian, barrier and other path-dependent options;
• short rate models and interest rate derivatives;
• convertible bonds;
• stochastic volatility and jumps;
• volatility derivatives;
• foreign exchange and commodity derivatives.

More information: Course Website STA 2503.

Prerequisite:  Knowledge of undergraduate probability theory is necessary. Knowledge of basic financial modeling (e.g., binomial trees and log-normal distributions), introductory stochastic calculus and financial products is useful, but not necessary. This course moves at a faster pace, is more advanced and contains a higher workload than STA2502, only students who are well prepared will be allowed to take this course. It is also distinct from STA 2047 which instead focuses on the mathematics of stochastic analysis.  This course requires instructor approval prior to enrolment.

In this course we will study techniques and algorithms for creating effective data visualizations based on principles from graphic design, visual art, perceptual psychology, and cognitive science.This course is targeted both towards students interested in using visualization in their own work, as well as students interested in building better visualization tools and systems.

Please note that STA3000Y F & S can only be taken by PhD students in the Department of Statistical Sciences.

This is the Department’s core graduate course in statistical theory. It covers the basic principles of statistical inference, their application to a variety of statistical models, and some generalizations to more complex settings.

Prerequisite:

• STA2112H and STA2212H or equivalent. (STA2111H and STA2211H may be co-requisites).
• Some familiarity with measure theory is very useful. The text includes some supplementary material on this.

Nonstandard analysis provides a rigorous foundation for carrying out mathematical analysis with the aid of infinitesimal numbers and other structures that appear in so-called saturated models of the real numbers. This course introduces nonstandard analysis using concepts and examples from statistics and probability. Topics include: extension, transfer, and saturation; infinitesimal and infinite numbers; hyperfinite sets and measures; hyperfinite models of stochastic processes; nonstandard Bayesian decision theory and connections to frequentism. Background in real analysis, probability theory, and statistics recommended. No background will be assumed in mathematical logic.

Prerequisite: Mathematical maturity, including real analysis and probability theory. MSC with instructor approval.

TBA

Consult the instructor for further details.

Prerequisite: Consult the instructor concerning necessary background for this course.

(also offered as undergraduate course STA437H1)

Practical techniques for the analysis of multivariate data; fundamental methods of data reduction with an introduction to underlying distribution theory; basic estimation and hypothesis testing for multivariate means and variances; regression coefficients; principal components and the partial multiple and canonical cor relations; multivariate analysis of variance;  classification and the linear discriminant function. The use of R software should be  expected.

(also offered as undergraduate course STA447H1)

Discrete and continuous time processes with an emphasis on Markov, Gaussian and renewal processes. Martingales and further limit theorems. A variety of applications taken from some of the following areas are discussed in the context of stochastic modeling: Information Theory, Quantum Mechanics, Statistical Analyses of Stochastic Processes, Population Growth Models, Reliability, Queuing Models, Stochastic Calculus, Simulation (Monte Carlo Methods).

Recommended Preparation: knowledge of probability theory calculus and basic real analysis.

(also offered as undergraduate course STA465H1)

Data acquisition trends in the environmental, physical and health sciences are increasingly spatial in character and novel in the sense that modern sophisticated methods are required for analysis. This course will cover different types of random spatial processes and how to incorporate them into mixed effects models for Normal and non-Normal data. Students will be trained in a variety of advanced techniques for analyzing complex spatial data and, upon completion, will be able to undertake a variety of analyses on spatially dependent data, understand which methods are appropriate for various research questions, and interpret and convey results in the light of the original questions posed.

(also offered as undergraduate course STA410H1)

The goal of this course is to give an overview of some of the computational methods that are useful in statistics. The rst part of the course will focus on basic algorithms, such as the Fast Fourier Transform (and related methods) and methods for generating random variables. The second part of the course will focus on numerical methods for linear algebra and optimization (for example, computing least squares estimates and maximum likelihood estimates). Along the way, you will learn some basic theory of numerical analysis (computational complexity, convergence rates of algorithms) and you will encounter some statistical methodology that you may not have seen in other courses.

Recommended Preparation: Background in statistics, computer programming, and linear algebra can be useful for this course.

(also offered as undergraduate course STA414H1)

This course will consider topics in statistics that have played a role in the development of techniques for data mining and machine learning. We will cover linear methods for regression and classification, nonparametric regression and classification methods, generalized additive models, aspects of model inference and model selection, model averaging and tree bassed methods.

The course will focus on generalized linear models (GLM) and related methods, such as generalized additive model involving nonparametric regression, generalized estimating equations (GEE) and generalized linear mixed models (GLMM) for longitudinal data. This course is designed for Master and PhD students in Statistics, and is REQUIRED for the Applied paper of the PhD Comprehensive Exams in Statistics. We deal with a class of statistical models that generalizes classical linear models to include many other models that have been found useful in statistical analysis, especially in biomedical applications. The course is a mixture of theory and applications and includes computer projects featuring R (S+) or/and SAS programming.

Topics: Brief review of likelihood theory, fundamental theory of generalized linear models, iterated weighted least squares, binary data and logistic regression, epidemiological study designs, counts data and log-linear models, models with constant coefficient of variation, quasi-likelihood, generalized additive models involving nonparametric smoothing, generalized estimating equations (GEE) and generalized linear mixed models (GLMM) for longitudinal data.

(also offered as undergraduate course STA457H1)

An overview of methods and problems in the analysis of time series data. Topics include: descriptive methods, filtering and adjustment, spectral estimation, bivariate time series models.

The course will cover the following topics:

• Theory of stationary processes, linear processes
• Elements of inference in time domain with applications
• Spectral representation of stationary processes
• Elements of inference in frequency domain with applications
• Theory of prediction (forecasting) with applications > ARMA processes, inference and forecasting
• Non-stationarity and seasonality, ARIMA and SARIMA processes

Further topics, time permitting: multivariate models; GARCH models; state-space models

STA 2211H is a follow-up course to STA 2111H, designed for Master’s and Ph.D. level students in statistics, mathematics, and other departments, who are interested in a rigorous, mathematical treatment of probability theory using measure theory. Specific topics to be covered include: weak convergence, characteristic functions, central limit theorems, the Radon-Nykodym Theorem, Lebesgue Decomposition, conditional probability and expectation, martingales, and Kolmogorov’s Existence Theorem.

This course is a continuation of STA2112H. It is designed for graduate students in statistics and biostatistics.

Topics include:

• Likelihood inference
• Bayesian methods
• Significance testing
• Linear and generalized linear models
• Goodness-of-fit
• Computational methods

Prerequisite: STA2112H

This course is designed to provide graduate students with experience in statistical consulting. Students are active participants in research projects brought to the Statistical Consulting Service (SCS) of the Department of Statistics. The course is offered over the two sessions, fall (September-December) and winter (January-April). The overall workload is approximately equivalent to a half graduate course and students receive a half credit.

Students are not expected to have had any experience as consultants. The purpose of the course is to provide this experience so that graduates will be better able to function in such an environment when they have completed the course. The course also provides students with the opportunity to become familiar with statistical software packages such as The SAS System. There is supervision and assistance to novice consultants.

Content: There is some classroom instruction at the start of the term, an d meetings occasionally are called to discuss special topics and for students to compare experiences. Students serve as apprentice statisticians and work under the guidance of the instructor and the SCS Coordinator on individual projects. Projects are assigned to students as they come in to the SCS. There are periods of inactivity when there are no projects and other times are very busy. The pattern of work is more like that associated with a business or working environment than a traditional course. While some consideration is taken of other academic demands on students, those enrolling must be aware that work on projects may require precedence at times.

Evaluation: Students will be graded on the quality of their work as stati stical consultants. This involves the ability to do work in a timely fashion, the quality of advice provided and the quality of the presentation of advice and written work to clients.

Recommended Preparation: Students should have taken some applied sta tistics courses such as an undergraduate regression course. Also undergraduate courses in applied statistics, sample survey, design of experiments and time series analysis are recommended but these are not required. Also taking some of the other 2000 level applied statistics courses is recommended as this course will serve as an excellent opportunity to put the content of these courses to work.

(also offered as undergraduate course ACT466H1)

Limited fluctuation or American credibility, on a full and partial basis. Greatest accuracy or European credibility, predictive distributions and the Bayesian premium, credibility premiums including the Buhlmann and Buhlmann-Straub models, empirical Bayes nonparametric and semi-parametric parameter estimation. Simulation, random numbers, discrete and continuous random variable generation, discrete event simulation, statistical analysis of simulated data and validation techniques.

Recommended Preparation: Consult the instructor concerning necessary background for this course.

Please note that STA3000Y F & S can only be taken by PhD students in the Department of Statistical Sciences.

This is the Department’s core graduate course in statistical theory. It covers the basic principles of statistical inference, their application to a variety of statistical models, and some generalizations to more complex settings.

Prerequisite:

• STA2112H and STA2212H or equivalent. (STA2111H and STA2211H may be co-requisites).
• Some familiarity with measure theory is very useful. The text includes some supplementary material on this.

Inference based on the likelihood function has a prominent role in both theoretical and applied statistics. This course will introduce some of the more recent developments in likelihood-based inference, with an emphasis on adaptations developed for models with complex structure or large numbers of nuisance parameters. Special emphasis will be given to applications in biology and medicine throughout the course. Tentative topics to be covered include: review of likelihood inference and asymptotic results; adjustments to profile likelihood; misspecified models — composite likelihood; partially specified models — quasi-likelihood; properties and limitations of penalized likelihood.

This course explores the replication of financial derivatives from the standpoint of investment banks ("sell-side") and the application of derivatives from the standpoint of pension funds, insurers, hedge funds, mutual funds and private equity funds ("buy-side").
The course is structured into three components:

1. The first module analyses how trading and structuring desks at investment banks use vanilla options to create bespoke payouts for institutional investors, corporates and retail investors.

2. The second module examines how the buy-side uses derivatives for:

• Hedging: e.g., protecting traditional balanced portfolios, managing currency risk ;
• Outperforming benchmarks: currency & equity overlay;
• Expressing “macro” views on equity indices, rates, currencies & commodities;
• Expressing “micro” views on sectors & single stocks;
• And addresses why investor preferences give rise to risk premia, and how derivatives can be structured to take advantage of persistent behavioural biases in the market.

3. The third module synthesizes the key learnings from 1. and 2. into case studies