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 correlations; multivariate analysis of variance;  classification and the linear discriminant function. The use of R software should be expected.

(also offered as undergraduate course STA465H1)
 

Data acquisition in the environmental, physical, and health sciences are increasingly spatial, and novel in the sense that specialized methods are required for analysis. This course will cover different types of spatial and spatiotemporal data and their analytic methods. Students will learn a variety of advanced techniques for analyzing geostatistical, areal, and point referenced data. Focus will be placed on visualizing spatial data, choosing the correct method for a specific research question, and communicating analytic results clearly and effectively.

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.

This course is designed to give an overview of some of the computational methods that are useful in statistics. The first 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.

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 part one of a 2-course sequence that introduces graduate students to computational methods designed specifically for statistical inference. This course will cover methods for optimization and simulation methods in several contexts. Optimization methods are introduced in order to conduct likelihood-based inference, while simulation techniques are used for studying the performance of a given statistical model and to conduct Bayesian analysis. Covered topics include gradient-based optimization algorithms (Newton method, Fisher scoring), the Expectation-Maximization (EM) algorithm and its variants (ECM, MCEM, etc), basic simulation principles and techniques for model analysis (cross-validation independent replications, etc), Monte Carlo and Markov chain Monte Carlo algorithms (accept-reject, importance sampling Metropolis-Hastings and Gibbs samplers, adaptive MCMC, Approximate Bayesian computation, consensus Monte Carlo, subsampling MCMC, etc). Particular emphasis will be placed on modern developments that address situations in which the Bayesian analysis is conducted when data are massive or the likelihood is intractable. The focus of the course is on correct usage of these methods rather than the detailed study of underlying theoretical arguments.

TBD

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.

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 beneficial. The text includes supplementary material on this topic.

This course will cover current topics in Data Science from a statistical perspective. The exact topics will vary from year to year. Emphasis will be on practical aspects of data science. This could include tools, workflows, reproducibility, and communication through a statistical lens but not all topics will be covered exhaustively every year.

(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 correlations; 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.

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.

(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-based methods.

Statistical inference is concerned with using the evidence, available from observed data, to draw inferences about an unknown probability measure. A variety of theoretical approaches have been developed to address this problem and these can lead to quite different inferences. A natural question is then concerned with how one determines and validates appropriate statistical methodology in a given problem. 

This course presents mathematical foundations for learning, prediction, and decision making. Unlike in traditional statistical learning, however, our focus will be on notions of optimality that do not rely on stochastic modeling assumptions on data. A primary focus will be on learning from data to compete with a class of baselines predictors/strategies, often referred to as experts. A secondary focus will be on the ability to adapt to the presence or absence of statistical patterns, without presuming at the outset that such patterns will arise. Topics include: regret; prediction with expert advice; the role of the loss function in tight bounds; online classification; online linear and convex optimization; regularization; bandit problems/decisions with limited feedback; minimax optimality and adaptivity; relationships with statistical learning.

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

STA2211H 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

The course will discuss the technical side of statistical methods focusing on two key aspects: optimization and implementation. The first part of the course will introduce necessary background for understanding and devising algorithms for modern statistical methodology. It will cover core concepts and tools from convex optimization such as convexity of sets and functions, Lagrange multipliers method, Newton’s method, proximal gradient descent, coordinate descent, alternating direction method of multipliers. In addition, it will include the review of key topics in linear algebra such as matrix and vector norms, quadratic forms and positive semidefinite matrices, matrix calculus (gradient, Hessian and determinant), matrix decompositions (QR, Cholesky, eigen and singular value). The second part of the course will focus on topics from statistical methodology with an emphasis on computational aspects. The covered concepts will include model assessment and selection (bias-variance trade-off, cross-validation and bootstrap), feature selection (penalized generalized linear models, elastic net, group and fused lasso, least angle regression), dimension reduction (principal component analysis, independent component analysis, factor analysis), data compression (k-means, hierarchical, and spectral clustering). The course will involve a significant practical component, which will include labs and coding assignments where students will master their skills in implementing statistical optimization algorithms.

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.

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.

An overview of theory and methods in the analysis of survival data. Topics include survival distributions and their applications, parametric and non-parametric methods, proportional hazards regression, and extensions to competing risks and multistate modelling.

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.

This course provides an introduction to a scholarly approach to teaching statistics in higher education. Emphasis is placed on the use of statistics education research, effective communication of fundamental statistical concepts typically encountered in introductory statistics, alignment of learning outcomes, course activities and assessments, recognition of common misconceptions and how to address them, and effective integration of educational and statistical technologies. No prior teaching experience is necessary.

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.