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.

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.

(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.

(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.

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.

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.

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.