Students are advised that they should discuss their academic background with the instructor before or at the first meeting of the course. Consult the timetable for the meeting information for each course.

Note: 1000 level courses cannot be taken for by graduate students in the Department of Statistics.

### STA1001H – Applied Regression Analysis (also offered as undergraduate course STA302H1)

Introduction to data analysis with a focus on regression. Initial Examination of data. Correlation. Simple and multiple regression models using least squares. Inference for regression parameters, confidence and prediction intervals. Diagnostics and remedial measures. Interactions and dummy variables. Variable selection. Least squares estimation and inference for non-linear regression.

*Prerequisite:* STA248H1/261H1/ECO220Y1(70%)/ ECO227Y1/(STA257H1/(STA250H1, STA255H1))

### STA1003H – Sample Surveys Theory (also offered as undergraduate course STA304H1)

Design of surveys, sources of bias, randominized response surveys. Techniques of sampling; stratification, clustering, unequal probability selection. Sampling inference, estimates of population mean and variances, ratio estimation., observational data; correlation vs. causation, missing data, sources of bias.

*Exclusion: *STA322H1

*Prerequisite: *ECO220Y1/ECO227Y1/GGR270Y1 / PSY202H1/SOC300Y1/STA221H1/STA255H1/261H1/248H1

### STA1004H – Elementary Experimental Design (also offered as undergraduate course STA305H1)

This cross-listed course covers a number of topics used in the design and analysis of experiments. The course is intended for students of statistics as well as students of other disciplines (eg. engineering, experimental science, etc.) who will use experimental design and analysis in their work.

The course will cover the following topics: randomization, blocking Latin squares, balanced incomplete block designs, factorial experiments, confounding and fractional replication, components of variance, orthogonal polynomials, response surface methods. Additional topics will be covered based on students’ interest as time permits.

*Prerequisite:* STA302H/352Y/ECO327Y/ECO357Y or permission of instructor.

### STA1005H – Applied Multivariate Analysis (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; regressi on coefficients; principal components and the partial multiple and canonical cor relations; multivariate analysis of variance; profile analysis and curve fitting for repeated measurements; classification and the linear discriminant function. There will be extensive use of statistical computing packages.

*Prerequisite: *STA302H/352Y

*Recommended Preparation: *MAT223H/240H

### STA1007H – Statistics for Life and Social Scientists (also offered as undergraduate course STA429H1)

Consult the instructor for further details.

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

### STA1008H -Applied Statistics

Vocabulary of data analysis, Tests of statistical significance, Principles of research design, Introduction to unix, Introduction to SAS, Elementary significance tests, Multiple regression, Factorial ANOVA, Permutation tests, Power and sample size, Random effects models, Multivariate analysis of variance, Analysis of within-cases designs (repeated measures). If time permits, Categorical data analysis.

*Prerequisite*: Any introductory statistics class, taught by any department.

### STA2004H Design of Experiments

A second course in design of experiments. Topics include: experiments vs observational studies, randomization and model-based inference, randomized blocks, Latin squares, incomplete block designs, factorial and fractional factorial designs, cross-over designs, confounding and aliasing, response surface designs and Taguchi methods, optimal design, Bayesian design.

*Prerequisite:* STA332H or equivalent

### STA2006H Applied Stochastic Processes (also offered as undergraduate course STA447H1)

Detailed information provided by the instructor. Suggested topics to be covered include Markov chains, renewal theory, queueing theory, martingales, and Brownian motion.

*Prerequisite:* STA347H or equivalent knowledge of probability theory; and MAT235Y/237Y or equivalent knowledge of multivariate calculus and basic real analysis.

### STA2101H Methods of Applied Statistics I (also offered as undergraduate course STA442H1)

Advanced topics in statistics and data analysis with emphasis on applications. Diagnostics and residuals in linear models, introductions to generalized linear models, graphical methods, additional topics such as random effects models, split plot designs, analysis of censored data, introduced as needed in the context of case studies.

*Prerequisite*: ECO374H1/ECO375H1/STA302H1; STA305H1

### STA2102H Computational Techniques in Statistics (also offered as undergraduate course STA410H1)

This course will study how statistical computations are done, and develop students’ abilities to write programs for statistical problems that are not handled by standard packages. Students will learn the capabilities of the R statistical computing environment, and learn to program new statistical methods in that environment. R will be introduced as part of the course; no prior knowledge of it is necessary.

*Prerequisite: *This course is designed for graduate and senior undergraduate students in statistics, actuarial science, computer science or other fields where statistical computation is important.

Students should have a basic background in statistical methods (eg. at the level of STA302), and some prior experience with programming (eg. at the level of CSC108).

### STA2104H Statistical Methods for Machine Learning and Data Mining (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.

*Prerequisite: *Either STA302H or CSC411H

### STA2105H **Nonparametric methods of inference** (also offered as undergraduate course STA412H1)

Modern methods of nonparametric inference, with special emphasis on bootstrap methods, and including density estimation, kernel regression, smoothing methods and functional data analysis.

Prerequisite: STA302H1, STA352Y1

### STA2111H Graduate Probability I

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.

### STA2112H Mathematical Statistics I

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.

*Prerequisite: *Advanced calculus (eg. MAT237) and linear algebra (eg. MAT223, MAT224). A previous course in probability and/or statistics is highly recommended.

### STA2162H Statistical Inference I (also offered as undergraduate course STA422H1)

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.

*Necessary background*: Mathematics-based course on the theory of statistics (e.g., at the level of STA352Y).

### STA2201H Methods of Applied Statistics II

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.

*Prerequisite:* Advanced Calculus, Linear Algebra, STA 347 and STA 422 (upper-division courses on probability and statistical inference) or equivalent, STA 302 (linear regression), Statistical Computing using R (S+) or/and SAS (alternative softwares are allowed). However, please be advised that I may not be familiar with the software of your choice resulting in limited assistance.

### STA2202H Time Series Analysis (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

### STA2209H Lifetime Data Modeling and Analysis

Students interested in this may wish to take the course, Survival Analysis, offered by the Department of Public Sciences, Biostatistics program.

### STA2211H Graduate Probability II

STA 2211H is a follow-up course to STA 2111F, 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.

### STA2212H Mathematical Statistics II

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

A continuation of STA2112. Topics include: Bayesian methods, minimum variance estimation, asymptotic efficiency of maximum likelihood estimation, interval estimation and hypothesis testing, linear and generalized linear models, goodness-of-fit for discrete and continuous data.

*Prerequisite:* STA2112

### STA2453HY Statistical Consulting

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.

*Prerequisite:* 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.

### STA2500H Loss Models (also offered as undergraduate course ACT451H1)

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

### STA2501H Mathematical Risk Theory

Consult the instructor for further details.

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

### STA2502H Stochastic Methods for Actuarial Science (also offered as undergraduate course ACT460H1)

Consult the instructor for further details.

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

### STA2503H Applied Probability for Mathematical Finance

This course features studies in derivative pricing theory and focuses on building basic financial theory and their applications to various derivative products. A working knowledge of probability theory, stochastic calculus, knowledge of ordinary and partial differential equations and familiarity with the basic financial instruments is assumed. The topics covered in this course include, but are not limited to: fixed income products; forwards and futures; binomial pricing model; 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.

Enrolment is strictly limited, please consult the instructor for more details.

*Prerequisite:* STA347H and ACT460H or equivalent. Knowledge of undergraduate probability theory, introductory stochastic calculus and financial products.

### STA2505H Credibility Theory & Simulation Methods (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.

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

### STA2542H Linear Models

This is an advanced graduate course. The emphasis is on linear mixed models and generalized mixed models. Inference requires numerical optimization methods Newton-Raphson and EM algorithms) as well as Monte Carlo sampling methods (importance sampling, accept-reject, Metropolis-Hastings, Gibbs) and these will be taught in class.

*Prerequisite: *Strong background in Statistics is required.

### STA3000Y Advanced Theory of Statistics

STA3000Y is the Department’s core graduate course in statistical theory that all Ph.D. students are required to take. M.Sc. students who have the requisite background are also encouraged to take this course. The course 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.

### STA3431H Monte Carlo Methods

This course will explore Monte Carlo computer algorithms, which use randomness to perform difficult high-dimensional computations. Different types of algorithms, theoretical issues, and practical applications will all be considered. Particular emphasis will be placed on Markov chain Monte Carlo (MCMC) methods. The course will involve a combination of methodological investigations, mathematical analysis, and computer programming.

*Prerequisite: * Knowledge of statistical inference and probability theory at the advanced undergraduate level, and familiarity with basic computer programming techniques.

### STA4273H Research Topics in Bayesian Inference

Consult the instructor for further details.

### STA4247H Point Processes, noise and stochastic analysis

Introduction to the theory of point processes – Poisson and compound processes, point provesses with repulsion and attraction. Brownian motion, white noise. Stochastic intergration and stochastic differential equtions.

Rationale: Point processes and noise are a central area in probability and statistics. A grade course on this topic is much needed.

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

### STA4xxxH Research Topics in Statistics

Topic announced each year. Consult the instructor for further details.

*Prerequisite: *Permission of the instructor

### Master’s Research Project Course

A limited number of Supervised Research Project courses, normally taken as half-courses, will also be made available, based on faculty availability. These courses will provide students with a first exposure to research-level topics and thinking. Students will normally be required to write a substantial report about their work, plus perhaps give a brief oral presentation. Projects may be proposed either by faculty or by students; information about faculty-proposed projects will be provided in September.

To enroll in such a course, a student must first obtain permission from the supervising faculty member and from the Associate Chair, Graduate Studies. There is no guarantee that enrollment can be provided for all interested students. For further details, please consult the Associate Chair, Graduate Studies.