## Statistics, Faculty of Arts and Sciences

### STAT: Statistics

STAT 121 (3) Elementary Statistics
Descriptive and inferential statistics, elementary probability, probability distributions, estimation of parameters, hypotheses testing, correlation, linear regression. Cannot provide credit towards a B.Sc. degree. Good for CA, CMA credit. Credit will be granted for only one of STAT 121, STAT 124, or STAT 230. [3-1-0]
Prerequisite: Foundations of Mathematics 11.
Introduction to surveys and simple sampling strategies; descriptive methods for one and two variables; frequency distributions; correlation and regression; descriptive methods for time series and index numbers; and probability and relationship to statistical inference. Good for CA, CMA credit. Credit will be granted for only one of STAT 121, STAT 124, or STAT 230. [3-1-0]
Prerequisite: One of Principles of Mathematics 11, Pre-Calculus 11, Foundations of Mathematics 12.
STAT 230 (3) Introductory Statistics
Applied statistics for students with a first-year calculus background. Estimation and testing of hypotheses, problem formulation, models and basic methods in analysis of variance, linear regression, and non-parametrics. Descriptive statistics and probability are presented as a basis for such procedures. Credit will be granted for only one of STAT 121, STAT 124, or STAT 230. [3-1-0]
Prerequisite: One of MATH 101, MATH 142.
STAT 240 (3) Statistical Reasoning
Simple and multiple linear regression, calibration, nonlinear regression, analysis of variance, factorial experiments, nonparametric methods, and basic quality control charts. [3-1-0]
Prerequisite: STAT 230.
STAT 303 (3) Introduction to Probability
Basic notions of probability, random variables, expectation and conditional expectation and limit theorems. [3-0-0]
Prerequisite: MATH 200.
Equivalency: MATH 302.
STAT 309 (3) Introduction to Statistical Inference
Review of probability theory. Sampling distributions. Large sample theory and methods of estimation and hypothesis testing, including maximum likelihood estimation, likelihood ratio testing, and confidence interval construction. [3-0-0]
Prerequisite: All of STAT 230, STAT 303.
STAT 310 (3) Regression Analysis
Theory and application of regression analysis, including residual analysis, diagnostics, transformations, model selection and checking, weighted least squares, and nonlinear models. Additional topics may include inverse, robust, ridge, and logistic regression. [3-1-0]
Prerequisite: All of STAT 230, MATH 221.
STAT 311 (3) Modern Statistical Methods
Bootstrap, jackknife, permutation tests, additive models, scatterplot smoothers, projection-pursuit regression, neural networks, tree-based methods, nonparametric methods, unsupervised methods. [3-0-0]
Prerequisite: STAT 230.
STAT 336 (3) Statistical Quality Control
Basic concepts and terminology, modern approach to quality, control charts, process capability analysis, measurement process control and calibration, and experimental design. [3-1-0]
Prerequisite: STAT 230.
STAT 400 (3) Statistical Communication and Consulting
Development of broad guidelines for a comprehensive approach to data analysis with a focus on communicating statistical ideas from planning experiments to the presentation of results. Topics include criteria for selection of suitable methodologies, data preparation, outlier detection, and exploratory data analysis. Credit will be granted for only one of DATA 500 or STAT 400 when the subject matter is of the same nature. [3-0-0]
Prerequisite: DATA 311, and fourth-year standing in the Data Science major or honours program.
STAT 401 (3) Probability and Statistical Inference
Formal introduction to the theory of statistical modeling with a focus on distributions of data, likelihood based inference for learning unknown parameters, construction of confidence intervals and development of tests. Bayesian methods will be used to contrast standard statistical procedures. [3-1-0]
Prerequisite: All of STAT 230, STAT 303.
STAT 403 (3) Stochastic Processes
Random walks, Markov chains, Poisson processes, continuous time Markov chains, birth and death processes, exponential models, and applications of Markov chains. [3-0-0]
Prerequisite: STAT 303.
STAT 405 (3) Design and Analysis of Experiments
Theory and application of the analysis of variance for standard experimental designs. Single factor designs, fixed and random effects, block designs, hierarchical designs, multiple comparisons, Cochran's theorem, factorial design, mixed models, general rules of the analysis of balanced designs, and analyses of covariance. [3-1-0]
Prerequisite: All of STAT 230, MATH 221.
STAT 406 (3) Environmetrics
Foundation of the use of statistical concepts and methods in environmental science and management. Scientific problem-solving using statistical methods. Integration of the formulation of objectives, study design, and quantitative methods appropriate for the design. The role and use of statistical software packages. [3-0-0]
Prerequisite: STAT 230.
STAT 407 (3) Sample Surveys
Planning and practice of sample surveys. Random sampling; bias and variance; unequal probability sampling; systematic, multistage, and stratified sampling; ratio and regression estimators; post-stratification; establishing a frame; pretesting; pilot studies; nonresponse; and additional topics. Credit will be granted for only one of STAT 407 or STAT 507. [3-0-0]
Prerequisite: All of STAT 230, STAT 303.
STAT 410 (3) Introduction to Generalized Linear Models
Logistic regression, probit regression, binomial regression, Poisson regression, overdispersion, quasi-likelihood, and the exponential family. [3-1-0]
Prerequisite: STAT 310.
STAT 448 (3/6) d Directed Studies in Statistics
Investigation of a specific topic as agreed upon by the student and the faculty supervisor. Completion of a project and an oral presentation are required. No more than 6 credits of STAT 448 may be taken for credit.
Prerequisite: Successful completion of 15 credits of 300- or 400-level MATH and STAT courses; and permission of the unit and faculty supervisor.
STAT 449 (3-9) d Special Topics in Statistics
Students should consult with the unit to determine the availability of specific topics to be offered under the direction of a staff member. May be taken more than once with different topics.
Prerequisite: Permission of the unit.
STAT 507 (3) Sampling and Design
Collection of data using either designed experiments or survey samples. Planning and practice of data collection. Observational and experimental data pros and cons. Standard methods in survey samples. Experimental design review. Credit will be granted for only one of STAT 407 or STAT 507.
STAT 538 (3) Advanced Statistical Modelling
Least-squares, generalized least-squares and likelihood estimation. Theory and application of parametric and non-parametric regression models such as splines, penalized splines, and generalized additive models. Assessment and treatment of data issues including missingness and measurement error. Credit will be granted for only one of DATA 410 or STAT 538. [3-2-0]
STAT 547 (2-15) d Topics in Statistics
Topics will be chosen from different areas within the field of statistics, such as time series, longitudinal and multi-level modelling, multivariate analysis, machine learning, resampling and permutation methods, smoothing and filtering, survival analysis, sports analytics and spatial statistics. Content will be determined so as to complement course offerings and meet the needs of the students. With the permission of the unit, this course may be taken more than once on a different topic. [3-0-0]
STAT 560 (3) Probability and Stochastic Processes
Theory of probability, including random variables, expectation, conditional expectation, generating functions, modes of convergence of random variables and their distributions. Applications to random models such as Markov, Poisson, birth-death, Gaussian and diffusion processes. [3-0-0]

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