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.

Statistical genetics is an important data science research area with direct impact on population health, and this course provides an introduction to its concepts and fundamentals. We start with an overview of genetic studies to have a general understanding of its goal and study design. We then introduce the basic genetic terminologies necessary for the ensuing discussion of the various statistical methods used for analyzing genetic data. The specific topics include population genetics, principles of inheritance, likelihood for pedigree data, aggregation, heritability, and segregation analyses, map and linkage analysis, population-based and family-based association studies and genome-wide association studies. The flow of the content generally follows that of the "The Fundamentals of Modern Statistical Genetics" by Laird and Lange, and additional materials will be provided. Participating students do not need formal training in genetics, but they are expected to have statistical knowledge at the level of STA303H1 Methods of Data Analysis II or equivalent.

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.

The goal of this course is 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.

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.

This is a course designed for master's and PhD 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.

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.

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. The course considers this larger statistical question. This involves a discussion of topics such as model specification and checking, the likelihood function and likelihood inferences, repeated sampling criteria, loss (utility) functions and optimality, prior specification and checking, Bayesian inferences, principles, and axioms, etc. The overall goal of the course is to leave students with an understanding of the different approaches to the theory of statistical inference while developing a critical point-of-view.

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's 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.

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 aims to introduce model selection methods for survival time and recurrent event data analysis. Topics include parametric models for lifetime and recurrent event data, regression models, parametric, semiparametric and nonparametric inference, goodness-of-fit and model selection. With applications to statistics, actuarial science, biostatistics, and engineering.

This is a follow-up course to STA2111H, designed for master's and PhD 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.

This course is part one of a two-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.

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. The course is offered over the two sessions, Fall (September to December) and Winter (January to 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.

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.

Consult the instructor for further details.

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.

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, for example, STA2502H), 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.

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.

An overview of methods and problems in the analysis of time series data related to finance and insurance. The course will focus on both theory and application with real datasets using R and Python and will require writing reports. Topics include stationary processes, linear processes; elements of inference in time and frequency domains with applications; ARMA, ARIMA, SARIMA, ARCH, GARCH; filtering and smoothing time-series; and State-space models.

This graduate course develops the theory and application of life insurance products. Beginning with basic life insurance and annuity valuation, the course introduces the concepts of premium reserving, multiple decrements, multiple life insurance, and expense loading. As well, topics in pension mathematics will be covered. The course and projects emphasize numerical implementation and practical relevance.

This course focuses on data science techniques for risk modelling stemming from finance and insurance, including maximum likelihood estimation, expectation maximization, generalized linear and additive models, mixture models, hidden Markov models, artificial neural networks, and reinforcement learning.

This course features studies in the risks, and how to quantify and manage those risk, in financial and mortality linked insurance products. Topics include: hedging of guarantees embedded in equity-linked insurance and annuity products, asset-liability management, determination of regulatory and economic capitals, insurance securitization (life and P/C), longevity bonds and derivatives, reinsurance, catastrophe bonds and derivatives.

This course explores what are the various issues that arise when machine and statistical learning methods are used in practice on big data to inform business intelligence (in finance and insurance). In practice, data is not clean, number of features is large, feature engineering must be carried out, and data is often multi-modal consisting not only of structured data, but also of images, text, and social network data. In this course, students will be exposed to various techniques and practical know-how to deal with these cases and learn how to present results to practitioners who are not domain experts.

This course extends over the Fall/Winter semesters and will feature invited guest speakers delivering both academic and practical seminars on current aspects of finance and insurance modeling, pensions, valuation risk management, regulation, and accounting.

This course takes cases from a variety of problems in the financial and insurance worlds and students will work in groups to develop both the theory and implementation of cases, write reports, and deliver presentations on their findings. The course will be led by industry practitioners. Sample topics include: Solvency II, Pension Benefits Act, valuing and managing complex annuity riders.

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.