37 graduate courses in the Spring 2025 Graduate Calendar.
STAT 631Introduction to Statistical Methods in Health Informatics0.50 units
Exploratory data analysis and data visualization. Confounding, censoring, selection bias, study designs and meta-analysis. Statistical modelling for continuous and binary data. Use of a statistics package, such as SAS, to analyze case studies will be important throughout. This is open only to students registered in the Masters of Health Informatics plan.
STAT 814Systematic Review and Meta-Analysis0.50 units
This course will provide students with an overview of the rationale and stages involved in the conduct of a formal systematic review and meta-analysis of a well-defined clinical/health research question. The overarching aim is to provide students with the tools to critically appraise and conduct a systematic review and meta-analysis. Students will largely work in pairs to progress through each step involved (with feedback from instructors at each stage) and to produce a final systematic review and meta-analysis to be presented/submitted at the end of the course. Course Objectives: 1. To demonstrate an understanding of the rationale underlying a systematic review and meta-analysis and relevance to clinical care and health policy; 2. To critically appraise a systematic review; 3. To develop a focused research question amenable to a systematic review; 4. To develop and implement a comprehensive and systematic literature search strategy; 5. To determine and apply procedures for including/excluding potential studies for a systematic review and meta-analysis; 6. To develop and implement a data abstraction process and study database; 7. To demonstrate an understanding of the fundamental statistical/biostatistical issues relevant to the conduct of a formal systematic review and meta-analysis. 8. To perform statistical analyses for a systematic review and meta-analysis and complete/present a final report demonstrating all stages involved. Students will need to meet with Course Coordinators and provide of appropriate previous experience with linear and/or logistic regression techniques.
Review of experimental designs in a regression setting; analysis of variance; replication, balance, blocking, randomization, and interaction; one-way layout, two-way layout, and Latin square as special cases; factorial structure of treatments; covariates; treatment contrasts; two-level fractional factorial designs; fixed versus random effects; split-plot and repeated-measures designs; other topics.
STAT 831Generalized Linear Models and Applications0.50 units
Review of normal linear regression and maximum likelihood estimation. Computational methods, including Newton-Raphson and iteratively reweighted least squares. Binomial regression; the role of the link function. Goodness-of-fit, goodness-of-link, leverage. Poisson regression models. Generalized linear models. Other topics in regression modelling.
This course provides further ideas and methods in stochastic modelling, with an emphasis on continuous-time stochastic processes. Topics cover time to absorption based quantities and discrete phase-type distributions of discrete-time Markov chains, continuous-time Markov chains with a countable state space, limit distributions for ergodic and absorbing chains, and applications including birth and death processes and queueing models of practical interest. Other topics may include continuous phase-type distributions, renewal theory and limit theorems for regenerative processes, and phase-type renewal processes.
STAT 835Statistical Methods for Process Improvement0.50 units
Statistical methods for improving processes based on observational data. Assessment of measurement systems. Strategies for variation reduction. Process monitoring, control and adjustment. Clue generation techniques for determining the sources of variability. Variation transmission.
STAT 836Introduction to the Analysis of Spatial Data in Health Research0.50 units
The objective of this course is to develop understanding and working knowledge of spatial models and analysis of spatial data. The course provides an introduction to the rudiments of statistaical inference based on spatially correlated data. Methods of estimation and testing will be developed for geostatistical models based on variograms and spatial autoregressive models. Concepts and application of methods will be emphasized through case studies and projects with health applications.
Prerequisites
Complete 1 of the following
Must have completed the following:
STAT831 - Generalized Linear Models and Applications (0.50)
Introduction to and application of computational methods in statistical inference. Monte Carlo evaluation of statistical procedures, exploration of the likelihood function through graphical and optimization techniques. Topics include expectation-maximization, bootstrapping, Markov Chain Monte Carlo, and other computationally intensive methods.
STAT 841Statistical Learning - Classification0.50 units
Classification is the problem of predicting a discrete outcome from a set of explanatory variables. Main topics include logistic regression, neural networks, tree-based methods, support vector machines and nearest neighbour methods. Other topics include model assessment, training and tuning.
Visualization methods applied to data. Both human perception and statistical properties inform the methods used to display and visually explore categorical, continuous, time-ordered, map, and high dimensional data. Order and layout effects on tables and graphics. Statistical concepts visually presented include variability, densities, quantiles, conditioning, and hypothesis testing. Interactive graphics include linking, brushing, motion, and the navigation of high dimensional spaces guided via projection indices. Glyphs (e.g. cartoon, statistical, or heatmap) and radial and parallel coordinates.
STAT 844Statistical Learning - Advanced Regression0.50 units
This course introduces modern applied regression methods for continuous response modelling, emphasizing both explainability and predictive power. Topics cover a wide selection of advanced methods useful to address the challenges arising from real-world and high-dimensional data; methods include robust regression, nonparametric regression such as smoothing splines, kernels, additive models, tree based methods, boosting and bagging, and penalized linear regression methods such as the ridge regression, lasso, and their variants. Students will gain an appreciation of the mathematical and statistical concepts underlying the methods and also computational experience in applying the methods to real data.
STAT 845Statistical Concepts for Data Science0.50 units
This is a foundational survey course designed for Data Science students who do not have an undergraduate degree in statistics. It provides an understanding and appreciation of the essential statistical concepts needed for Data Science. It has modular design with the following modules: probability for statistics, concepts of statistical inference, simulation and Monte Carlo methods, regression modelling, planning empirical studies, and drawing conclusions from data. Emphasis will be on exposing students to the core concepts and illustrating them largely through examples.
This course introduces Data Science students to exploratory data analysis with a focus on the concepts and tools necessary for understanding and successfully undertaking an end to end exploratory analysis of large and complex data. All stages of data collection, preparation and cleaning, importation into a statistical programming environment, data manipulation, as well as analysis and visualization will be treated. Material will be presented via case studies which will involve hands on programming and analysis. Methods and models (both statistical and computational) will be introduced as needed according to the nature of the data encountered in each case. The case studies will be chosen to give a breadth of experience to the student. A modern statistical programming language will be used throughout.
STAT 850Estimation and Hypothesis Testing0.50 units
Discussion of inference problems under the headings of hypothesis testing and point and interval estimation. Frequentist and Bayesian approaches to inference. Construction and evaluation of tests and estimators. Large sample theory of point estimation.
Sources of survey error. Probability sampling designs, estimation and efficiency comparisons. Distribution theory and confidence intervals. Generalized regression estimation. Software for survey analysis.
This course acts as a capstone on the coursework based part of the PhD program and as a stepping stone to the PhD proposal and to research. It is aimed at developing research skills: critically reading published research, summarizing and synthesizing areas of research, writing and orally presenting summaries of research problems, data sets and theoretical and applied results. The course is designed to be integrative across core areas of the student discipline.
Review of conditioning on sigma-fields; martingale theory (discrete and continuous-time) and applications; counting processes; Brownian motion; stochastic differential and integral equations and applications; general theory of Markov processes (including martingale problems and semigroup theory), diffusions; weak convergence of stochastic processes on function spaces; functional versions of the central limit theorem and strong laws; convergence of empirical processes.
Antirequisites
Not completed nor concurrently enrolled in any of the following:
STAT 906Computer Intensive Methods for Stochastic Models in Finance0.50 units
Review of basic numerical methods. Simulation of random variables, stochastic processes and stochastic models in finance. Numerical solution of deterministic and stochastic differential equations. Valuation of complex financial instruments and derivative securities. Project and paper.
Asymptotic theory for statistical procedures, such as modes of convergence, Big O, small o calculus, concentration of measures, laws of large numbers, different types of central limit theorems. Parametric, nonparametric, and high-dimensional inference, optimal statistical procedures. Theory of computationally intensive methods, advances in hypothesis testing.
This is an in-depth and rigorous course on Bayesian methods for statistical analysis and inference. Topics include fundamentals of Bayesian reasoning: prior and posterior distributions, Bayesian decision theory; Bayesian point and interval estimation, hypothesis testing, model selection, predictive distributions, large sample theory; and Bayesian approaches to topics such as regression, hierarchical models, high-dimensional problems, nonparametrics, latent variable modelling and computational techniques.
Multivariate normal and Wishart distributions, estimation and hypothesis testing of mean vectors and covariance matrices and their extensions to high-dimensional setting (n<p), principal component analysis (PCA), factor analysis, canonical analysis, discrimination, and classification with a focus on linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA). Precision matrices for high-dimensional data, high dimensional, and sparse PCA, Nonlinear PCA.
Multiple time series modeling including transfer function and intervention analysis. Various special topics in time series such as outliers, robustness, order determination methods, Kalman filtering, sampling and aggregation, seasonal adjustments.
STAT 931Causal Inference and Epidemiological Studies0.50 units
Causal inference in health research will be covered. Methods for the design and analysis of randomized controlled trials including randomization techniques, sample size and power calculations, and specialized additional topics including missing data, noncompliance, and ethics. The design and analysis of classical and modern epidemiological studies will then be discussed for settings in which randomization is not feasible. Causal inference methodologies for the analysis of observational data include propensity scores, marginal structural models and instrumental variables. Studies will be discussed from the epidemiological literature and other sources in the public domain. Simulations and data analyses will be carried out using software (e.g. R or SAS). Students will be trained and assessed in part based on the preparation of reports and delivery of presentations.
STAT 932Classification and Prediction in High Dimensional Analysis in Health Research0.50 units
In this course, we will cover classification and prediction in health research with a view to applications to screening and diagnosis of disease. This will lead to methods for evaluating the performance of various types of statistical models and learning techniques/algorithms. Cross-validation and bootstrap approaches will be introduced for model performance evaluation, and we will discuss discrimination and calibration as different components of prediction performance. We will cover variable selection techniques, including for high-dimensional data, with an emphasis on regularization techniques such as the LASSO and its variants. Model validation, both internal and external, and model updating will be covered, and we will also discuss post-model selection inference. An important focus will be on biomarker evaluation for a given disease, potentially connected to therapy, and leading to coverage of precision/personalized medicine. Finally, there will be coverage on the importance of reproducible and replicable research. Examples from different problems in health, including genetics, will be presented, and software (e.g. R or SAS) will be used throughout the course.
This course deals with methods of analyzing data on the time to failure with particular emphasis on the use of regression models for such data. Both parameteric and semi-parametric regression models will be considered.
This course covers methods for analyzing data in which repeated measures have been obtained for individuals in health studies over time. Different methods will be discussed to handle both continuous and discrete longitudinal response data, with examples from biomedical and population health datasets. Some of the approaches covered will include linear, non-linear, and generalized linear mixed effects models, as well as generalized estimating equations and transition models, with distinctions drawn between subject-specific and population averaged approaches for generalized linear longitudinal response data. Also, there will be coverage of exploratory methods, evaluation of model assumptions and adapting to assumption violations, approaches for handling missing data, and treatment of advanced topics such as semiparametric and nonparametric models for longitudinal data. Software (e.g. R or SAS) will be used throughout the course.
This course will cover some of the basic tools of a statistical consultant. Topics will include the use of statistical packages, problem-solving techniques, discussion of common statistical consulting problems, effective communication of statistical concepts and management of consulting sessions.
Deep learning uses artificial neural networks to create representations of data with multiple levels of abstraction. Deep learning usually refers to a set of algorithms and computational models that are composed of multiple processing layers. These methods have significantly improved the state-of-the-art in many domains including Natural Language Processing (NLP), Natural Language Understanding (NLU), Speech Recognition, Computer Vision, Classification, Pattern Recognition and Bioinformatics. This course will cover the modern practice of deep networks, different architectures of deep networks including feed forward and convolutional models, methods for sequence modeling, variational and adversarial models, attention mechanism and optimization and regularization for deep models.
The focus of this course is on the statistical modelling, estimation and inference and forecasting of nonlinear financial time series, with a special emphasis on volatility and correlation of asset prices and returns. Topics to be covered normally include: review on distribution and dynamic behaviour of financial time series, univariate and multivariate GARCH processes, long-memory time-series processes, stochastic volatility models, modelling of extreme values, copulas, realized volatility and correlation modelling for ultra high frequency data and continuous time models.