Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.

Notes:

Not every 400- and 500-numbered Statistics course is offered every year. Check with the divisional office to plan for the upcoming cycle of offered courses.

For listings of related courses, see Actuarial Science, Applied Mathematics, Mathematics, and Pure Mathematics.

Effective Fall 2014, Mathematics 265, 267, 367, Mathematics 275, 277, 375 and 377 replaced respectively Mathematics 251, 253, 353, Applied Mathematics 217, 219, 307 and 309 and serves as prerequisites for appropriate courses. In some special cases, Mathematics 267 replaces Mathematics 349 or 353. For these and other deviations from the general rule, see individual course entries for details. Mathematics 267 supplemented by Mathematics 177 will be accepted as equivalent to Mathematics 277.

Junior Courses

Students requiring one course (3 units) in Statistics should take Statistics 205.

Statistics 205

Introduction to Statistical Inquiry

The systematic progression of statistical principles needed to conduct a statistical investigation culminating in parameter estimation, hypothesis testing, statistical modelling, and design of experiments. Course Hours:3 units; H(3-1T) Prerequisite(s):Mathematics 30-1 or Pure Mathematics 30 or Mathematics II (offered by Continuing Education) or registration in the Faculty of Nursing. Antirequisite(s):Credit for Statistics 205 and either 211 or 213 will not be allowed. Notes:See the statements regarding credit which appear at the beginning of the Statistics course listings. This course is highly recommended for Statistics Majors.

Collection and presentation of data, introduction to probability, including Bayes' law, expectations and distributions. Properties of the normal curve. Introduction to estimation and hypothesis testing. Course Hours:3 units; H(3-1-1T) Prerequisite(s):Mathematics 30-1 or Pure Mathematics 30 or Mathematics II (offered by Continuing Education). Notes: See the statements regarding credit which appear at the beginning of the Statistics course listings.

Estimation of population parameters; confidence intervals for means; choice of sample size. Tests of hypotheses including 2-sample tests and paired comparisons. The Chi-squared tests for association and goodness-of-fit. Regression and correlation; variance estimates; tests for regression and correlation coefficients. Non-parametric methods and associated tests. Time series, forecasting. Course Hours:3 units; H(3-1-1T) Prerequisite(s):Statistics 213. Notes: See the statements regarding credit which appear at the beginning of the Statistics course listings.

A calculus-based introduction to probability theory and applications. Elements of probabilistic modelling, Basic probability computation techniques, Discrete and continuous random variables and distributions, Functions of random variables, Expectation and variance, Multivariate random variables, Conditional distributions, Covariance, Conditional expectation, Central Limit Theorem, Applications to real-world modelling. Course Hours:3 units; H(3-1T) Prerequisite(s):Mathematics 267 or 277 or 253 or 283 or Applied Mathematics 219. Notes:Statistics 205 is strongly recommended as preparation for this course for Statistics majors. Also known as:(formerly Mathematics 321)

Statistics and their distributions. Introduction to statistical inference through point estimation and confidence interval estimation of a population parameter. Properties of statistics including unbiasedness and consistency in estimation. Single parameter hypothesis testing, Type I and Type II Errors. Multi-parameter estimation through confidence interval estimation and hypothesis testing. The analysis of bivariate data through simple linear regression, including inferences on the parameters of the linear model and the analysis of variance. Course Hours:3 units; H(3-1T) Prerequisite(s):Mathematics 321 or Statistics 321. Notes:Prior or concurrent completion of Mathematics 353 or 381 is strongly recommended for students without credit of Mathematics 267 or 277. Also known as:(formerly Mathematics 323)

Statistics for the Physical and Environmental Sciences

Introduction to the collection of data. Probability and probability distributions. Single and Multi-sample estimation of distribution parameters. Regression and Goodness of Fit tests. Experimental Design and Analysis of Variance. Course Hours:3 units; H(3-1) Prerequisite(s):Mathematics 249 or 251 or 265 or 275 or 281 or Applied Mathematics 217. Notes: See the statements regarding credit which appear at the beginning of the Statistics course listings.

An advanced examination of core concepts in mathematical statistics, including the multivariate normal distribution, limit distributions, sufficient statistics, completeness of families of distributions, exponential families, likelihood ratio tests, chi-square tests, and the analysis of variance. Additional topics and examples relating to sequential tests, non-parametric methods, Bayesian statistical modelling, and the general linear model may also be explored. Course Hours:3 units; H(3-0) Prerequisite(s):Statistics 323 or Mathematics 323; and Mathematics 267 or 277 or 353 or 381.

Introduction to questionnaire design of sample surveys. Treatment of the various sampling methodologies used in population parameter estimation. Ratio and regression estimation. Sampling weights and variance estimation of statistics. Estimation of population size and density. Non-response. Course Hours:3 units; H(3-1T) Prerequisite(s):One of Statistics 217, 323, 327, Engineering 319, Psychology 312, or Sociology 311.

Introduction to the design of experiments and the statistical analysis of data. Analysis of variance in the response variable and adequacy of the model. Multiple comparison methods. Extensions to completely randomized block, latin-squares, and factorial experimental design. Introduction to nested and split-plot design, with emphasis on statistical software usage. Course Hours:3 units; H(3-1T) Prerequisite(s):One of Statistics 217, 323, 327, Engineering 319, Psychology 312, or Sociology 311.

Multiple linear regression model, parameter estimation, simultaneous confidence intervals and general linear hypothesis testing. Residual analysis and outliers. Model selection: best regression, stepwise regression algorithms. Transformation of variables and non-linear regression. Applications to forecasting. Variable selection in high-dimensional data using linear regression. Computer analysis of practical real world data. Course Hours:3 units; H(3-1T) Prerequisite(s):Statistics 323 or Mathematics 323; and Mathematics 211 or 213.

Fundamental topics in biostatistics, including descriptive statistics, graphical presentation of data, analysis of variance (ANOVA), study designs, contingency tables, measures of association, tests of significance, categorical data analysis, regression, time to event data analysis. Course Hours:3 units; H(3-1T) Prerequisite(s):Statistics 323 or Mathematics 323.

An introduction to the theory and tools to conduct time series analysis, with the emphasis on modelling and forecasting using a software. Stationarity, white noise, autocorrelation, partial autocorrelation, and linear predictor. Stationary ARIMA models, seasonality and trends. Model fitting, diagnostics and forecasting. Additional topics may include state space models, spectral analysis of time series, and GARCH models. Course Hours:3 units; H(3-1T) Prerequisite(s):Statistics 429.

Markov chains. Limit distributions for ergodic and absorbing chains. Classification of states, irreducibility. The Poisson process and its generalizations. Continuous-time Markov chains. Brownian motion and stationary processes. Renewal theory. Course Hours:3 units; H(3-0) Prerequisite(s): Mathematics 321 or Statistics 321. Also known as:(formerly Statistics 407)

A capstone course intended for students in their final year of study. The emphasis is on how to address real world scientific and social issues by applying the various statistical methods acquired in the earlier years in a unified and appropriate way. This involves method selection, data handling, statistical computing, consulting, report writing and oral presentation, team work, and ethics. Course Hours:3 units; H(3-1) Prerequisite(s):Two of Statistics 423, 425, 429 and 505. Antirequisite(s):Credit for Statistics 517 and either 513 or 515 will not be allowed.

Fundamentals of Bayesian inference, single and multiparameter models, hierarchical models, regression models, generalized linear models, advanced computational methods, Markov chain Monte Carlo. Course Hours:3 units; H(3-0) Prerequisite(s):Statistics 323 or Mathematics 323; and Mathematics 267 or 277 or 353 or 381. Notes:Completion of Statistics 421 is highly recommended as preparation for this course.

Non-parametric estimation and tests of hypotheses. Distribution-free tests. Asymptotic Theory. Re-sampling method and density estimation. Course Hours:3 units; H(3-0) Prerequisite(s):Statistics 323 or Mathematics 323; and Mathematics 267 or 277 or 353 or 381. Notes: May not be offered every year. Consult the department for listings.

Normal distribution. Statistical inference: confidence regions, hypothesis tests, analysis of variance, simultaneous confidence intervals. Multivariate statistical methods; principal components, factor analysis, discriminant analysis and classification, canonical correlation analysis, cluster analysis. Course Hours:3 units; H(3-0) Prerequisite(s):Statistics 323. Notes:May not be offered every year. Consult the department for listings. Completion of Mathematics 311 or 313 is highly recommended as preparation for this course.

Content of the course will vary from year to year. Consult the Department for information on choice of topics. Course Hours:3 units; H(3-1) Prerequisite(s): Consent of the Department. MAY BE REPEATED FOR CREDIT

Introduction to statistical computing; random numbers generation; Monte Carlo methods (variance reduction technique; computation of definite integrals); Optimizations; Numerical integrations. Course Hours:3 units; H(3-1) Prerequisite(s):Statistics 323 or Mathematics 323; and Mathematics 267 or 277 or 353 or 381.

Nature and properties of survival models; methods of estimating tabular models from both complete and incomplete data samples including actuarial, moment and maximum likelihood techniques; estimations of life tables from general population data; Kaplan-Meier estimator and Nelson-Allan estimator; the accelerated failure time model; the Cox proportional hazards model; model building and high-dimensional survival data analysis. Course Hours:3 units; H(3-1T) Prerequisite(s):Statistics 323 or Mathematics 323. Also known as:(formerly Statistics 433)

Description and inference for binomial and multinomial observations using proportions and odds ratios; multi-way contingency tables; generalized linear models for discrete data; logistic regression for binary responses; multi-category logit models for nominal and ordinal responses; loglinear models, and inference for matched-pairs and correlated clustered data. Course Hours:3 units; H(3-1T) Prerequisite(s):Statistics 429.

Note: Some 500- and 600-level statistics courses may have concurrent lectures. Extra work in these courses (e.g., extra assignments, advanced examination questions, a term project) will be required for credit at the 600 level.

Statistics 600

Research Seminar

A professional skills course, focusing on the development of technical proficiencies that are essential for students to succeed in their future careers as practicing statistician in academia, government, or industry. The emphasis is on delivering professional presentations and using modern statistical research tools. A high level of active student participation is required. Course Hours:1.5 units; Q(3S-0) Also known as:(formerly Statistics 621) MAY BE REPEATED FOR CREDIT NOT INCLUDED IN GPA

The content of this course is decided from year to year in accordance with graduate student interest and instructor availability. Topics include but are not restricted to: Advanced Design of Experiments, Weak and Strong Approximation Theory, Asymptotic Statistical Methods, the Bootstrap and its Applications, Generalized Additive Models, Order Statistics and their Applications, Robust Statistics, Statistics for Spatial Data, Statistical Process Control, Time Series Models. Course Hours:3 units; H(3-0) MAY BE REPEATED FOR CREDIT

Advanced topics in survival models such as the product limit estimator, the cox proportional hazards model, time-dependent covariates, types of censorship. Course Hours:3 units; H(3-0)

Exponential family of distributions, binary data models, loglinear models, overdispersion, quasi-likelihood methods, generalized additive models, longitudinal data and generalized estimating equations, model adequacy checks. Course Hours:3 units; H(3-0)

Topics include but are not restricted to selections from: linear approximations; model specification; various iterative techniques; assessing fit; multiresponse parameter estimation; models defined by systems of differential equations; graphical summaries of inference regions; curvature measures. Course Hours:3 units; H(3-0)

Topics in advanced actuarial theory and practice, such as: insurance risk models; practical analysis of extreme values; advanced property and casualty rate making; actuarial aspects of financial theory. Course Hours:3 units; H(3-0) MAY BE REPEATED FOR CREDIT

Probability spaces, integration, expected value, laws of large numbers, weak convergence, characteristic functions, central limit theorems, limit theorems in Rd, conditional expectation, introduction to martingales. Course Hours:3 units; H(3-0) Prerequisite(s):Statistics 321 or Mathematics 321; and Mathematics 353 or 367 or 381.

Likelihood function and likelihood principle, sufficiency, completeness of exponential families, Cramer-Rao lower bound, Lehmann-Scheffe Theorem, Rao-Blackwell Theorem, estimation methods, basic asymptotic theory, consistent asymptotic normal estimators (CAN), asymptotic properties of the maximum likelihood estimators, Bayesian estimation. Course Hours:3 units; H(3-0) Prerequisite(s):Statistics 323 or Mathematics 323; and Mathematics 353 or 367 or 381.