A survey of statistical methodology with emphasis on the relationship between data analysis and probability theory. Topics covered include descriptive statistics, limit theorems, sampling distribution, point and interval estimation, hypothesis testing, contingency tables and count data, simple linear regression. A statistical computer package will be used.

A sequel to STA256H5 introducing current statistical theory and methodology. Topics include: Sampling distributions, point estimation, confidence intervals, testing (Neyman-Pearson Theorem, uniformly most powerful test, likelihood ratio tests), unbiasedness, consistency, sufficiency, complete statistics, and exponential family; Fisher Information and the Cramer-Rao inequality; simple linear models.

Analysis of the multiple regression model by least squares; statistical properties of the least square analysis, including estimation of error; residual and regression sums of squares; distribution theory under normality of the observations; confidence regions and intervals; tests for normality; variance stabilizing transformations, multicolinearity, variable search methods.

The sample survey is a widely used technique for obtaining information about a large population at relatively small cost. Only probability samples can provide both an estimator and a measure of sampling error from the data itself. In addition to sampling error, non-sampling errors (refusals, not-at-home, lies, inaccuracies, etc.) are always present, and can produce serious biases. The course covers: design of surveys, sources of bias, randomized 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.

This course covers topics in the design and analysis of experiments. The topics covered include analysis of variance, randomization, confounding, block designs, factorial designs, orthogonal polynomials and response surface methods. Applications include agricultural experiments, laboratory experiments, and industrial experiments, including quality control techniques.

Introduction to a topic of current interest in statistics. Content will vary from year to year. Computer packages are used. The contact hours for this course may vary in terms of contact type (L, T) from year to year, but will be between 36-48 contact hours in total. See the UTM Timetable.

Introduction to a topic of current interest in statistics. Content will vary from year to year. Computer packages are used. The contact hours for this course may vary in terms of contact type (L, T) from year to year, but will be between 36-48 contact hours in total. See the UTM Timetable.

A thorough introduction to the basic ideas in supervised statistical learning with a focus on regression and a brief introduction to classification. Methods covered will include multiple linear regression and its extensions, k-nn regression, variable selection and regularization via AIC,BIC, Ridge and lasso penalties, non-parametric methods including basis expansions, local regression and splines, generalized additive models, tree-based methods, bagging, boosting and random forests. Content will be discussed from a statistical angle, putting emphasis on uncertainty quantification and the impact of randomness in the data on the outcome of any learning procedure. A detailed discussion of the main statistical ideas behind crossvalidation, sample splitting and re-sampling methods will be given. Throughout the course, R will be used as software, a brief introduction will be given in the beginning.

The second part of the course will focus on basic ideas in classification problems including discriminant analysis and support vector machine, and unsupervised learning techniques such as clustering, principal component analysis, independent component analysis and multidimensional scaling. The course will also cover the modern statistics in the "big data" area. The high dimensional problems when p >> n and n >> p will be introduced. In addition, the students will be formed as groups to do data analysis projects on statistical machine learning and present their findings in class. This will prepare them for future careers in industry or academia.

Discrete Markov chains with a finite number of states, random walks, single-server queues, continuous-time Markov chains, Poisson processes, branching processes, birth and death process, M/M/n queues, Monte-Carlo simulation may be introduced.

A thorough introduction to statistics from a Bayesian perspective. Methods covered will include: the rules of probability, including joint, marginal, and conditional probability; discrete and continuous random variables; discrete and continuous random variables; Bayesian inferences for means and proportions; the simple linear regression model analyzed in a Bayesian manner; and (time permitting) a brief introduction to numerical methods such as the Gibbs sampler. Throughout the course, R will be used as software, a brief introduction will be given in the beginning.

Students explore a topic in statistics under the supervision of a faculty member. Interested students must consult with statistics faculty at least two months prior to registration, to determine the topic and scope.

Computational methods play a central role in modern statistics and machine learning. This course aims to give an overview of some of the computational techniques that are useful in statistics. Topics include methods of generating random variables, Monte Carlo integration and variance reduction, Monte Carlo methods in inference, bootstrap and jackknife, resampling application, permutation tests, probability density estimation, and optimization.

Introduction to a topic of current interest in statistics. Content will vary from year to year. The contact hours for this course may vary in terms of contact type (L, T) from year to year, but will be between 36-48 contact hours in total. See the UTM Timetable.

Students explore a topic in statistics under the supervision of a faculty member. Interested students must consult with statistics faculty at least two months prior to registration, to determine the topic and scope.

This course provides a richly rewarding opportunity for students in their third or fourth year to work in the research project of a professor in return for 399H course credit. Students enrolled have an opportunity to become involved in original research, learn research methods and share in the excitement and discovery of acquiring new knowledge. Participating faculty members post their project descriptions for the following summer and fall/winter sessions in early February and students are invited to apply in early March. See Research Opportunity Program (ROP) for more details.

This course provides a richly rewarding opportunity for students in their third or fourth year to work in the research project of a professor in return for 399Y course credit. Students enrolled have an opportunity to become involved in original research, learn research methods and share in the excitement and discovery of acquiring new knowledge. Participating faculty members post their project descriptions for the following summer and fall/winter sessions in early February and students are invited to apply in early March. See Research Opportunity Program (ROP) for more details.

This course covers advanced topics in probability and mathematical statistics. Topics include convergence in probability, convergence in distribution, and convergence with probability one, sufficiency, completeness, Rao-Blackwell and Lehmann-Sheffe theorems, and asymptotics.

Random vectors and matrices, univariate and multivariate regression with measurement error, latent variables, model identification, the LISREL model, path analysis,confirmatory factor analysis, longitudinal data analysis,robustness of the normal model. A statistical computing package will be used.

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; regression coefficients; principal components and the partial multiple and canonical correlations; 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.

Vocabulary of data analysis, Tests of statistical significance, Principles of research design, Applications of statistical methods such as Multiple regression, Factorial ANOVA, Mixed linear models, Multivariate analysis of variance, Repeated measures, Logistic regression, Generalized linear models, Permutation tests and Bootstrapping.

This course develops the theory and methodology for the statistical analysis of time series. The methods may be broadly characterized as time domain methods based on correlation (Box-Jenkins), or frequency domain methods based on a decomposition of the series into cycles (Fourier). The course develops both of these to the point where they may be applied using standard statistical software. Model identification, estimation and forecasting are discussed. Applications in social and physical sciences are used.

Students explore a topic in statistics under the supervision of a faculty member. Interested students must consult with statistics faculty at least two months prior to registration, to determine the topic and scope.

Introduction to a topic of current interest in statistics. Content will vary from year to year.The contact hours for this course may vary in terms of contact type (L, T) from year to year, but will be between 36-48 contact hours in total. See the UTM Timetable.

Students explore a topic in statistics under the supervision of a faculty member. Interested students must consult with statistics faculty at least two months prior to registration, to determine the topic and scope.

This course provides a richly rewarding opportunity for students in their third or fourth year to work in the research project of a professor in return for 499H course credit. Students enrolled have an opportunity to become involved in original research, learn research methods and share in the excitement and discovery of acquiring new knowledge. Participating faculty members post their project descriptions for the following summer and fall/winter sessions in early February and students are invited to apply in early March. See Research Opportunity Program (ROP) for more details.

This course brings together first-year students to explore a current topic or problem at the intersection of science and social science in a small-group environment. The focus of each section will depend on the instructor’s areas of expertise and will provide students with the opportunity to develop foundational learning strategies and sharpen their academic skills to support the transition into university. Students participate in a series of tutorials that will help them build foundational skills for academic success such as creating study plans, taking notes, reading critically, and developing a growth mindset.

This course brings together first-year students to explore a current topic or problem at the intersection of science and humanities in a small-group environment. The focus of each section will depend on the instructor’s areas of expertise and will provide students with the opportunity to develop foundational learning strategies and sharpen their academic skills to support the transition into university. Students participate in a series of tutorials that will help them build foundational skills for academic success such as creating study plans, taking notes, reading critically, and developing a growth mindset.

This course is an introduction to the common problem-solving tools used in the sciences and social sciences. It is designed to address the fundamental skills needed for comprehension and effective communication in these areas. The skills being addressed may include critical analysis of texts (primary literature, review papers, textbooks), use of databases to gather, manipulate and visualize data; interpretation and presentation of data; information gathering and writing skills (lab reports, critical essays); and oral presentations. Specific examples will be drawn from a variety of current research topics in both the sciences and social sciences. Students participate in a series of tutorials that will help them build foundational skills for academic success such as creating study plans, taking notes, reading critically, and developing a growth mindset.

This interdisciplinary course encourages students to take ownership of their education through a focus on the process of learning how to learn and by cultivating the habits of mind for lifelong achievement and success. Students will explore theories of learning and research on the strategies students should employ to reach deep understanding. "Science of Learning" is designed to help students develop their critical thinking, university-level oral and written communication, critical reading, and other foundational academic skills. Students participate in a series of tutorials that will help them build foundational skills for academic success such as creating study plans, taking notes, reading critically, and developing a growth mindset.