## Statistics

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Recent Courses

**Description:** Random variables and frequency distributions. Averages and variance. The binomial and normal distribution. Sampling distributions and elementary inference. X2-test for contingency tables. Regression and correlation. Analysis of variance. Prerequisite: Mathematics 30-1 or 30-2, or consent of Department. This course may not be taken for credit if credit has been obtained in any STAT course, or in PEDS 309, PSYCO 211 or SOC 210.

**Description:** 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. This course may not be taken for credit if credit has been obtained in any STAT course, or in PEDS 109, PSYCO 211, SCI 151 or SOC 210.

**Description:** Probability models; distribution of one and two random variables; moment generating functions; specific distributions; uniform, binomial, geometric, Poisson, exponential, normal, etc. Markov chains and simple queues. Various applications are considered with emphasis on the analysis of computer systems; simulation techniques are used and the algorithmic approach is used throughout the course. Restricted to Honors and Specialization students in Computing Science and Specialization students in Computational Science (Mathematics). Prerequisites: MATH 101 or 115 or 118 or SCI 100 or equivalent; pre- or corequisite: MATH 102 or 120 or 125 or 127 or equivalent. Credit may not be obtained for both STAT 221 and STAT 265.

**Description:** Sampling distributions; estimation; hypothesis testing; linear regression. Poisson process; simple queues; models and applications which are primarily of interest to computing scientists. Prerequisite: STAT 221. Note: Credit may be obtained for at most one of STAT 222, 266 and 366.

**Description:** 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. Credit may not be obtained in STAT 235 if credit has already been obtained in STAT 141, 151, 222, 265, 266; PSYCO 211, SCI 151 or SOC 210. Intended for Engineering students. Other students who take this course will receive *3.0.

**Description:** 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. Credit may not be obtained in STAT 235 if credit has already been obtained in STAT 141, 151, 222, 265, 266; PSYCO 211, SCI 151 or SOC 210. Intended for Engineering students. Other students who take this course will receive *3.0.

**Description:** 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. Credit may not be obtained in STAT 235 if credit has already been obtained in STAT 141, 151, 222, 265, 266; PSYCO 211, SCI 151 or SOC 210. Intended for Engineering students. Other students who take this course will receive *3.0.

**Description:** 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. Credit may be received in at most one of STAT 252, 319, 337, or 341. May not be taken for credit if credit has been received for STAT 368 or 378. Prerequisite: STAT 141 or 151 or 235 or SCI 151 or equivalent.

**Description:** 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: MATH 214 or 217. Credit may not be obtained for both STAT 265 and STAT 221.

**Description:** 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. Prerequisite: STAT 265. Corequisites: MATH 215 or 317, and 225 or 227. Credit may not be obtained for both STAT 266 and either of STAT 222 or STAT 366.

**Description:** Reviews and extends those topics in the prerequisite courses in calculus and linear algebra which are of particular interest in Mathematical Statistics. These include the basics of mathematical reasoning as evidenced by the presentation of rigorous arguments, notions of continuity, differentiation, Riemann-Stieltjes integration and numerical optimization, and diagonalization results for real symmetric matrices. Applications to statistical theory will include least squares estimation, generating functions, and distribution theory. Prerequisites: MATH 215, 225 and STAT 266.

**Description:** Control charts for variables and attributes. Process capability analysis. Acceptance sampling: single and multiple attribute and variable acceptance plans. Prerequisite: STAT 235 or 265.

**Description:** 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 or SCI 151 and a 200-level Biological Science course. Note: This course may not be taken for credit if credit has already been obtained in STAT 252, 368 or 378.

**Description:** Time at death random variables, continuous and discrete insurances, endowments and varying annuities, net premiums and reserves. Prerequisites: MATH 253 and STAT 265. Corequisite: MATH 215.

**Description:** Analysis of benefits reserves, multiple life functions, multiple decrement models, applications of multiple decrement theory. Prerequisite: STAT 353. May be offered in alternate years.

**Description:** Utility theory, insurability of risk, the economics of insurance, the ratemaking process, IBNR and chain ladder method, property/casualty loss reserving techniques. Prerequisite: MATH 215, 253, and STAT 265. May be offered in alternate years.

**Description:** Simple random sampling from finite populations, stratified sampling, regression estimators, cluster sampling. Note: This course may only be offered in alternate years. Prerequisite: STAT 266, or STAT 235 and consent of instructor.

*No description available for this course.*

**Description:** 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. Prerequisites: STAT 266, or STAT 235 and consent of instructor.

**Description:** 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.

**Description:** 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.

**Description:** 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. Prerequisites: STAT 266, or STAT 235 and consent of instructor.

**Description:** Required by all students who have just completed a Mathematical Sciences Industrial Internship Program and who are in an Honors or Specialization degree in Statistics. Must be completed during the first academic term following return to full-time studies. Note: A grade of F to A+ will be determined by the student's job performance as evaluated by the employer, by the student's performance in the completion of an internship practicum report, and by the student's ability to learn from the experiences of the Internship as demonstrated in an oral presentation. Prerequisite: WKEXP 953.

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

**Description:** 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. Prerequisites: STAT 368 or 378.

**Description:** 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.

**Description:** Topics in actuarial mathematics, as selected by the instructor. Prerequisite: STAT 353 or MATH 353. This course may be offered in alternate years.

**Description:** Credibility theory: limited fluctuation; Bayesian; Buhlmann, Buhlmann-Straub; empirical Bayes parameter estimation; statistical inference for loss models; maximum likelihood estimation; effect of policy modifications; model selection. Prerequisite: STAT 453. This course may be offered in alternate years.

**Description:** 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: STAT 371.

**Description:** Sequences of Bernoulli trials, laws of large numbers, normal approximations. Generating functions, recurrent events, random walks. Introduction to Markov chains. Special topics. Prerequisite: STAT 471.

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

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** Topics in actuarial mathematics, as selected by the instructor. Prerequisite: Consent of the Department.

**Description:** Credibility theory: limited fluctuation; Bayesian; Buhlmann, Buhlmann-Straub; empirical Bayes parameter estimation; statistical inference for loss models; maximum likelihood estimation; effect of policy modifications; model selection. Prerequisite: Consent of the Department.

*No description available for this course.*

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

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

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** 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.

**Description:** Zero-one laws, sums of independent random variables, three-series criterion, laws of iterated logarithm, laws of large numbers, convergence in distribution, characteristic functions. Bochner's theorem, central limit theorems, discrete time martingales. Prerequisite: STAT 571 or MATH 543 or equivalent.

**Description:** Martingales and martingale inequalities, stopping theorems, local martingales, quadratic variation. Wiener and Poisson processes, stochastic integration. Ito's formula, semimartingales, Girsanov's theorem, introduction to stochastic differential equations, Markov processes, diffusion. Prerequisite: STAT 671 or equivalent.

**Description:** The autocorrelation function and spectrum and their estimates. Linear stationary models; autoregressive, moving average, and mixed models. Linear nonstationary models; autoregressive integrated moving average models. Forecasting. Model identification and estimation. Spectral analysis. Prerequisite: STAT 479 or equivalent.

*No description available for this course.*

*No description available for this course.*

*No description available for this course.*

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

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

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

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