# STAT - Statistics

Offered By:

Faculty of Science

Below are the courses available from the STAT code. Select a course to view the available classes, additional class notes, and class times.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Data collection and presentation, descriptive statistics. Probability distributions, sampling distributions and the central limit theorem. Point estimation and hypothesis testing. Correlation and regression analysis. Goodness of fit and contingency table. Prerequisite: Mathematics 30-1 or 30-2. Note : This course may not be taken for credit if credit has been obtained in any STAT course, or in KIN 109, PEDS 109, PSYCH 211, SCI 151 or SOC 210.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Data collection and presentation, descriptive statistics. Probability distributions, sampling distributions and the central limit theorem. Point estimation and hypothesis testing. Correlation and regression analysis. Goodness of fit and contingency table. Use of a microcomputer software package for statistical analyses in business and economics. Prerequisite: Mathematics 30-1 or 30-2. This course may not be taken for credit if credit has been obtained in any STAT course, or in KIN 109, PEDS 109, PSYCH 211, PTHER 352, SCI 151 or SOC 210.

**★ 3 (fi 6)(EITH/SP/SU, 3-0-1.5)**

Descriptive data analysis. Calculus of Probability. Binomial, multinomial, Poisson, normal, beta, exponential, gamma, hypergeometric, and Weibull distributions. Sampling distributions. Estimation, testing hypotheses, goodness-of-fit tests, and one-way analysis of variance. Linear correlation and regression. Sampling. Quality control. Use of a microcomputer software package for statistical analyses in engineering applications. Prerequisite: MATH 100. Corequisite: MATH 101. Notes: (1) This course may not be taken for credit if credit has already been obtained in one of STAT 141, 151, 222, 265, 266; PSYCH 211, SCI 151 or SOC 210. (2) Intended for Engineering students. Other students who take this course will receive *3.0.

## Starting: 2024-09-01 STAT 235 - Introductory Statistics for Engineering

**★ 3 (fi 6)(EITH/SP/SU, 3-0-1.5)**

Descriptive data analysis. Calculus of Probability. Binomial, multinomial, Poisson, normal, beta, exponential, gamma, hypergeometric, and Weibull distributions. Sampling distributions. Estimation, testing hypotheses, goodness-of-fit tests, and one-way analysis of variance. Linear correlation and regression. Sampling. Quality control. Use of a microcomputer software package for statistical analyses in engineering applications. Prerequisite: MATH 100. Corequisite: MATH 101. Notes: (1) This course may not be taken for credit if credit has already been obtained in one of STAT 141, 151, 222, 265, 266; PSYCH 211, SCI 151 or SOC 210. (2) Intended for Engineering students. Other students who take this course will receive 3.0 units.

## Starting: 2024-09-01 STAT 235 - Introductory Statistics for Engineering

**★ 3 (fi 6)(EITH/SP/SU, 3-0-1.5)**

Descriptive data analysis. Calculus of Probability. Binomial, multinomial, Poisson, normal, beta, exponential, gamma, hypergeometric, and Weibull distributions. Sampling distributions. Estimation, testing hypotheses, goodness-of-fit tests, and one-way analysis of variance. Linear correlation and regression. Sampling. Quality control. Use of a microcomputer software package for statistical analyses in engineering applications. Prerequisite: MATH 100. Corequisite: MATH 101. Notes: (1) This course may not be taken for credit if credit has already been obtained in one of STAT 141, 151, 222, 265, 266; PSYCH 211, SCI 151 or SOC 210. (2) Intended for Engineering students. Other students who take this course will receive 3.0 units.

**★ 1.5 (fi 6)(EITH/SP/SU, 3-0-1.5)**

Descriptive data analysis. Calculus of Probability. Binomial, multinomial, Poisson, normal, beta, exponential, gamma, hypergeometric, and Weibull distributions. Sampling distributions. Estimation, testing hypotheses, goodness-of-fit tests, and one-way analysis of variance. Linear correlation and regression. Sampling. Quality control. Use of a microcomputer software package for statistical analyses in engineering applications. Prerequisite: MATH 100. Corequisite: MATH 101. Notes: (1) This course may not be taken for credit if credit has already been obtained in one of STAT 141, 151, 222, 265, 266; PSYCH 211, SCI 151 or SOC 210. (2) Intended for Engineering students. Other students who take this course will receive *3.0.

## Starting: 2024-09-01 STAT 235A - Introductory Statistics for Engineering

**★ 1.5 (fi 6)(EITH/SP/SU, 3-0-1.5)**

Descriptive data analysis. Calculus of Probability. Binomial, multinomial, Poisson, normal, beta, exponential, gamma, hypergeometric, and Weibull distributions. Sampling distributions. Estimation, testing hypotheses, goodness-of-fit tests, and one-way analysis of variance. Linear correlation and regression. Sampling. Quality control. Use of a microcomputer software package for statistical analyses in engineering applications. Prerequisite: MATH 100. Corequisite: MATH 101. Notes: (1) This course may not be taken for credit if credit has already been obtained in one of STAT 141, 151, 222, 265, 266; PSYCH 211, SCI 151 or SOC 210. (2) Intended for Engineering students. Other students who take this course will receive 3.0 units.

**★ 1.5 (fi 6)(EITH/SP/SU, 3-0-1.5)**

Descriptive data analysis. Calculus of Probability. Binomial, multinomial, Poisson, normal, beta, exponential, gamma, hypergeometric, and Weibull distributions. Sampling distributions. Estimation, testing hypotheses, goodness-of-fit tests, and one-way analysis of variance. Linear correlation and regression. Sampling. Quality control. Use of a microcomputer software package for statistical analyses in engineering applications. Prerequisite: MATH 100. Corequisite: MATH 101. Notes: (1) This course may not be taken for credit if credit has already been obtained in one of STAT 141, 151, 222, 265, 266; PSYCH 211, SCI 151 or SOC 210. (2) Intended for Engineering students. Other students who take this course will receive *3.0.

## Starting: 2024-09-01 STAT 235B - Introductory Statistics for Engineering

**★ 1.5 (fi 6)(EITH/SP/SU, 3-0-1.5)**

**★ 3 (fi 6)(EITHER, 3-0-0)**

Methods in applied statistics including regression techniques, analysis of variance and covariance, and methods of data analysis. Applications are taken from Biological, Physical and Social Sciences, and Business. Prerequisite: One of STAT 141, 151, 161, 235 or SCI 151. Notes: (1) Credit can be obtained in at most one of STAT 252, 319, 337 or 341, or AREC 313. (2) This course may not be taken for credit if credit has already been obtained in STAT 368 or 378.

**★ 3 (fi 6)(FIRST, 3-0-0)**

Sample space, events, combinatorial probability, conditional probability, independent events, Bayes Theorem, random variables, discrete random variables, expected values, moment generating function, inequalities, continuous distributions, multivariate distributions, independence. Corequisite: One of MATH 209, 214 or 217. Note: Credit can be obtained in at most two of MATH 181, MATH 281, or STAT 265.

**★ 3 (fi 6)(SECOND, 3-0-0)**

Functions of random variables, sampling distributions, Central Limit Theorem, law of large numbers, statistical models for the data, likelihood, parameters and their interpretation, objectives of statistical inference, point and interval estimation, method of moments, basic notions of testing of hypotheses, errors of the first and second kind, significance level, power, p-value. Prerequisites: one of MATH 209, MATH 214, or MATH 217 and one of STAT 265 or MATH 281. Corequisites: One of MATH 225 or 227. Credit can only be obtained in one of STAT 266 or STAT 276.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Fundamental principles of statistical learning and inference for data science Understanding of types of analytics, probability, variability, relationship between variables, probability distributions, law of large numbers, Central Limit Theorem, hypothesis testing and statistical significance, and elementary theory of regression. Prerequisite: MATH 281 or STAT 265. Students presenting STAT 265 must also present one of MATH 117 or MATH 216 as corequisite. Credit can only be obtained in one of STAT 266 or STAT 276.

**★ 3 (fi 6)(FIRST, 3-0-2)**

Methods of data analysis useful in Biostatistics including analysis of variance and covariance and nested designs, multiple regression, logistic regression and log-linear models. The concepts will be motivated by problems in the life sciences. Applications to real data will be emphasized through the use of a computer package. Prerequisite: STAT 151, STAT 161, or SCI 151 and a 200-level Biological Science course. Notes : (1) Credit can be obtained in at most one of STAT 252, STAT 337, and AREC 313. (2) This course may not be taken for credit if credit has already been obtained in STAT 368 or 378.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Time at death random variables, continuous and discrete insurances, endowments and varying annuities, net premiums and reserves. Prerequisites: MATH 253 and one of STAT 265 or MATH 281.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Simple random sampling from finite populations, stratified sampling, regression estimators, cluster sampling. Prerequisite: One of STAT 266 or STAT 276, or STAT 235 with consent of the Department. Note: This course may only be offered in alternate years.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Basic principles of experimental design, completely randomized design-one way ANOVA and ANCOVA, randomized block design, Latin square design, Multiple comparisons. Nested designs. Factorial experiments. Prerequisite: One of STAT 266 or STAT 276, or STAT 235 with consent of the Department.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Problem solving of classical probability questions, random walk, gambler's ruin, Markov chains, branching processes. Selected topics of the instructor's choice. Prerequisite: STAT 265. Note: Credit can be obtained in at most one of MATH 281 or STAT 371.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Laws of large numbers, weak convergence, some asymptotic results, delta method, maximum likelihood estimation, testing, UMP tests, LR tests, nonparametric methods (sign test, rank test), robustness, statistics and their sensitivity properties, prior and posterior distributions, Bayesian inference, conjugate priors, Bayes estimators. Prerequisites: STAT 266 or STAT 276.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Simple linear regression analysis, inference on regression parameters, residual analysis, prediction intervals, weighted least squares. Multiple regression analysis, inference about regression parameters, multicollinearity and its effects, indicator variables, selection of independent variables. Non-linear regression. Prerequisite: One of STAT 266 or STAT 276, or STAT 235 with consent of the Department.

**★ 3 (fi 6)(SECOND, 3-0-0)**

Survey of contemporary languages/environments suitable for algorithms of Statistics and Data Science. Introduction to Monte Carlo methods, random number generation and numerical integration in statistical context and optimization for both smooth and constrained alternatives, tailored to specific applications in statistics and machine learning. Prerequisites: One of STAT 265 or MATH 281, or consent of the Department.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Survival models, model estimation from complete and incomplete data samples, parametric survival models with concomitant variables, estimation of life tables from general population data. Prerequisites: STAT 372 and 378.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Methods of data analysis useful in applied research, including repeated measures and longitudinal data analysis, non-linear regression, survival analysis, multivariate techniques. Applications to real data will be emphasized, including case studies and real data applications. Each researcher works on a project to present, highlighting the methods used in the project. Prerequisite: STAT 252 or 337 or consent of the instructor.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Review of linear and nonlinear regression and brief introduction to generalized linear models, the course covers selected methods of dimension reduction (principal components, factor analysis, canonical correlations), of unsupervised (clustering, multidimensional scaling ordination) and supervised classification (discriminant analysis, logistic regression, nearest neighbours - including, among others, the machine learning methods like classification trees, neural networks, and support vector machines). Prerequisite: STAT 378.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Classical ruin theory, individual risk models, collective risk models, models for loss severity: parametric models, tail behavior, models for loss frequency, mixed Poisson models; compound Poisson models, convolutions and recursive methods, probability and moment generating functions. Prerequisite: One of STAT 371 or MATH 281.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Probability spaces, algebra of events. Elements of combinatorial analysis. Conditional probability, stochastic independence. Special discrete and continuous distributions. Random variables, moments, transformations. Basic limit theorems. Prerequisite: One of STAT 371 or MATH 281.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Stationary series, spectral analysis, models in time series: autoregressive, moving average, ARMA and ARIMA. Smoothing series, computational techniques and computer packages for time series. Prerequisites: STAT 372 and 378. Note: This course may only be offered in alternate years.

**★ 3 (fi 6)(EITHER, 3-0-0)**

This course is designed to give credit to mature and able students for reading in areas not covered by courses, under the supervision of a staff member. A student, or group of students, wishing to use this course should find a staff member willing to supervise the proposed reading program. A detailed description of the material to be covered should be submitted to the Chair of the Department Honors Committee. (This should include a description of testing methods to be used.) The program will require the approval of both the Honors Committee, and the Chair of the Department. The students' mastery of the material of the course will be tested by a written or oral examination. This course may be taken in Fall or Winter and may be taken any number of times, subject always to the approval mentioned above. Prerequisite: Any 300-level STAT course.

**★ 3 (fi 6)(EITHER, 0-1S-6)**

This course provides students in Specialization and Honors programs an opportunity to pursue research in statistics under the direction of a member of the Department. Course requirements include at least one oral presentation and a written final report. Students interested in taking this course should contact the course coordinator two months in advance. Credit for this course may be obtained more than once. Prerequisites: a 300-level STAT course and consent of the course coordinator.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Basic principles of experimental design, completely randomized design-one way ANOVA and ANCOVA. Randomized block design. Latin square design, Multiple comparisons. Nested designs. Factorial experiments. Each student will give a written report and seminar presentation highlighting statistical methods used in a research project. Prerequisites: STAT 252 or 337 or equivalent and a course in linear algebra. Note: Cannot be used for credit towards a graduate program in Statistics.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Simple linear regression analysis, inference on regression parameters, residual analysis, prediction intervals, weighted least squares. Multiple regression analysis, inference about regression parameters, multicollinearity and its effects, indicator variables, selection of independent variables. Non-linear regression. Each student will give a written report and seminar presentation highlighting statistical methods used in a research project. Prerequisite: STAT 337 or equivalent and a course in linear algebra. Note: Cannot be used for credit towards a graduate program in Statistics.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Theory and applications of time series modelling, stationarity, autocorrelation. Spectral properties, filtering. Box-Jenkins models, seasonality. Each student will give a written report and seminar presentation highlighting statistical methods used in a research project. Prerequisite: STAT 372 and 378 or consent of Instructor.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Basic sampling schemes for finite populations: simple random sampling, stratified random sampling, systematic sampling and cluster sampling. Unequal probability sampling. Ratio and regression estimators. Prerequisite: A course in Statistical Inference at the 300 level or permission from the instructor. Note: Cannot be used for credit towards a graduate program in Statistics.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Principles of statistical model building and analysis applied in linear and generalized linear models and illustrated through multivariate methods such as repeated measures, principal components, and supervised and unsupervised classification. Each student will give a written report and seminar presentation highlighting statistical methods used in a research project. Prerequisites: STAT 501, 502 or equivalent. Note: Cannot be used for credit towards a thesis-based graduate program in Statistics.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Introduction to mathematical techniques commonly used in theoretical Statistics, with applications. Applications of diagonalization results for real symmetric matrices, and of continuity, differentiation, Riemann-Stieltjes integration and multivariable calculus to the theory of Statistics including least squares estimation, generating functions, distribution theory. Prerequisite: consent of Department.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Introduction to contemporary computational culture: reproducible coding, literate programming. Monte Carlo methods: random number generation, variance reduction, numerical integration, statistical simulations. Optimization (linear search, gradient descent, Newton-Raphson, method of scoring, and their specifics in the statistical context), EM algorithm. Fundamentals of convex optimization with constraints. Prerequisites: consent of the instructor.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Survival and hazard functions, censoring, truncation. Non-parametric, parametric and semi-parametric approaches to survival analysis including Kaplan-Meier estimation and Cox's proportional hazards model. Prerequisite: STAT 372 or consent of Department.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Review of basic statistical concepts of inference and probability theory. Includes applied methods of Linear and non-linear regression and analysis of variance for designed experiments, multiple comparisons, correlations, modeling and variable selection, multicollinearity, predictions, confounding and Simpson's paradox. Includes case studies and real data applications. Each researcher works on a project to present, highlighting the methods used in the project. Prerequisite: STAT 437 equivalent or consent of the instructor.

**★ 3 (fi 6)(EITHER, 3-0-0)**

The course focuses on statistical learning techniques, in particular those of supervised classification, both from statistical (logistic regression, discriminant analysis, nearest neighbours, and others) and machine learning background (tree-based methods, neural networks, support vector machines), with the emphasis on decision-theoretic underpinnings and other statistical aspects, flexible model building (regularization with penalties), and algorithmic solutions. Selected methods of unsupervised classification (clustering) and some related regression methods are covered as well. Prerequisite: Consent of the instructor.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Classical ruin theory, individual risk models, collective risk models, models for loss severity: parametric models, tail behavior, models for loss frequency, mixed Poisson models; compound Poisson models, convolutions and recursive methods, probability and moment generating functions. Prerequisite: STAT 371 or equivalent. Note: Cannot be used for credit towards a thesis-based graduate program in the Department of Mathematical and Statistical Sciences.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Review of basic sampling schemes: simple random sampling, and stratified random sampling, and systematic sampling. Multistage sampling schemes. Estimation of nonlinear parameters: ratios, regression coefficients, and correlation coefficients. Variance estimation techniques: linearization, BRR, jackknife, and bootstrap. Selected topics: model-based estimation, regression analysis from complex survey data. Relevant computer packages. Prerequisites: STAT 361, 372, 471.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Sampling models and methods of inference for discrete data. Maximum likelihood estimation for complete contingency tables, measures of association and agreement. Goodness-of-fit. Incomplete tables. Analysis of square tables; symmetry and marginal homogeneity. Model selection and closeness of fit; practical aspects. Chi-square tests for categorical data from complex surveys. Prerequisite: STAT 372 or 471.

**★ 3 (fi 6)(EITHER, 3-0-0)**

An introduction to the theory of statistical inference. Topics to include exponential families and general linear models, likelihood, sufficiency, ancillarity, interval and point estimation, asymptotic approximations. Optional topics as time allows, may include Bayesian methods, Robustness, resampling techniques. This course is intended primarily for MSc students. Prerequisite: STAT 471 or consent of Department.

**★ 3 (fi 6)(EITHER, 3-0-0)**

The general linear model. Fully randomized designs, one-way layout, multiple comparisons. Block designs, Latin squares. Factorial designs confounding, fractions. Nested designs, randomization restrictions. Response surface methodology. Analysis of covariance. Prerequisite: STAT 368 and a 400-level STAT course.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Measure and integration, Laws of Large Numbers, convergence of probability measures. Conditional expectation as time permits. Prerequisites: STAT 471 and STAT 512 or their equivalents.

**★ 3 (fi 6)(EITHER, 3-0-0)**

The multivariate normal distribution, multivariate regression and analysis of variance, classification, canonical correlation, principal components, factor analysis. Prerequisite: STAT 372 and STAT 512.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Multiple linear regression, ordinary and generalized least squares, partial and multiple correlation. Regression diagnostics, collinearity, model building. Nonlinear regression. Selected topics: robust and nonparametric regression, measurement error models. Prerequisites: STAT 378 and a 400-level statistics course.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Elements of stochastic processes. Discrete and continuous time Markov Chains; Birth and Death processes. Branching processes. Brownian Motion. General Stationary and Markov processes. Examples. Prerequisite: STAT 471 or consent of Instructor.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Data analysis, problem solving, oral communication with clients, issues in planning experiments and collecting data; practical aspects of consulting and report writing. Corequisite: STAT 568 and 578 or their equivalents.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Students will be supervised by an individual staff member to participate in areas of research interest of that staff member. Students can register only with the permission of the Chair of the Department in special circumstances. Will not be counted toward the minimum course requirement for graduate credits.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Advanced statistical design and methods. Topics include sampling, multivariate techniques, survival analysis, power and sample size, linear and non linear regression, longitudinal and repeated measures data, and analysis of seasonal or time series data. Topics to be covered can be influenced by the registered researchers. Includes critical review and case studies with real data applications. Each researcher works on a project to present, highlighting the methods used in the project. Prerequisite: STAT 537 or equivalent or consent of the instructor. Cannot be used for credit towards a graduate program in Statistics.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Modern methods of statistical inference. Various versions of likelihood: conditional, marginal, integrated, profile, partial, empirical. Estimating equations. Semi-parametric models. Foundational issues. Prerequisites: STAT 512 and 566.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Approximation techniques and asymptotic methods in statistics. Topics may include second and higher order expansions, asymptotics of likelihood based estimation and testing. Edgeworth expansions, exponential tilting, asymptotic relative efficiency, U-, M-, L-, and R-estimation. Prerequisites: STAT 566 or 664 and 512 or the equivalent.

**★ 3 (fi 12)(VAR, UNASSIGNED)**

Open only to students taking the MSc non-thesis option in statistics.

**★ 3 (fi 12)(VAR, UNASSIGNED)**

Open only to students taking the MSc non-thesis option in statistics.

**★ 1.5 (fi 3)(EITHER, UNASSIGNED)**

Open only to students taking the MSc non-thesis option in Statistics.

**★ 1.5 (fi 3)(EITHER, UNASSIGNED)**

Open only to students taking the MSc non-thesis option in Statistics.