A mathematically rigorous introduction to probability, with applications chosen to introduce concepts of statistical inference. Probability and expectation, discrete and continuous random variables and vectors, distribution and density functions, the law of large numbers. The binomial, geometric, Poisson, and normal distributions. The Central Limit Theorem. (Note: STA257H1 does not count as a distribution requirement course).

A rigorous introduction to the theory of statistical inference and to statistical practice. Statistical models, parameters, and samples. Estimators for parameters, sampling distributions for estimators, and the properties of consistency, bias, and variance. The likelihood function and the maximum likelihood estimator. Hypothesis tests and confidence regions. Examples illustrating statistical theory and its limitations. Introduction to the use of a computer environment for statistical analysis. (Note: STA261H1 does not count as a distribution requirement course).

Key areas of data science modeling including question formulation, data collection and cleaning, visualization, statistical inference, predictive modeling, and decision making.​ Through a strong emphasis on data-centric computing, quantitative critical thinking, and exploratory data analysis, this class covers key principles and techniques of data science. These include algorithms for statistical models and machine learning methods including regression, classification, neural networks, and clustering; principles behind creating informative data visualizations; and statistical concepts of measurement error and prediction.

Introduction to statistics and its connection to all stages of the scientific inquiry process. Issues around data collection, analysis and interpretation are emphasized to inform study design and critical assessment of published research. Statistical software is used to conduct descriptive and inferential statistics to address basic life sciences research questions.

Credit course for supervised participation in faculty research project. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities/research-opportunities-program. Not eligible for CR/NCR option.

Credit course for supervised participation in faculty research project. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities/research-opportunities-program. Not eligible for CR/NCR option.

Introduction to data analysis with a focus on regression. Initial Examination of data. Correlation. Simple and multiple regression models using least squares. Inference for regression parameters, confidence and prediction intervals. Diagnostics and remedial measures. Interactions and dummy variables. Variable selection. Least squares estimation and inference for non-linear regression.

Analysis of variance for one-and two-way layouts, logistic regression, loglinear models, longitudinal data, introduction to time series.

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.

Experiments vs observational studies, experimental units. Designs with one source of variation. Complete randomized designs and randomized block designs. Factorial designs. Inferences for contrasts and means. Model assumptions. Crossed and nested treatment factors, random effects models. Analysis of variance and covariance. Sample size calculations.

An introduction to data visualization and the use of visual and interactive representations of data to support human cognition. This course covers visualization techniques and algorithms based on principles from graphic design, perceptual psychology, cognitive science, and human-computer interaction. Topics include: graphic design, interaction, perception and cognition, communication, and ethics. Computational tutorials involve design review, implementation, and testing of information visualizations.

Statistical methods for supervised and unsupervised learning from data: training error, test error and cross-validation; classification, regression, and logistic regression; principal components analysis; stochastic gradient descent; decision trees and random forests; k-means clustering and nearest neighbour methods. Computational tutorials will support the efficient application of these methods.

An overview of probability from a non-measure theoretic point of view. Random variables/vectors; independence, conditional expectation/probability and consequences. Various types of convergence leading to proofs of the major theorems in basic probability. An introduction to simple stochastic processes such as Poisson and branching processes.

STA355H1 provides a unifying structure for the methods taught in other courses, and will enable students to read methodological research articles or articles with a large methodological component. Topics covered include statistical models and distributions; fundamentals of inference: estimation, hypothesis testing, and significance levels; likelihood functions and likelihood-based inference; prior distributions and Bayesian inference.

Bayesian inference has become an important applied technique and is especially valued to solve complex problems. This course first examines the basics of Bayesian inference. From there, this course looks at modern, computational methods and how to make inferences on complex data problems.

An instructor-supervised group project in an off-campus setting. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities/research-excursions-program. Not eligible for CR/NCR option.

An instructor-supervised group project in an off-campus setting. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities/research-excursions-program. Not eligible for CR/NCR option.

Credit course for supervised participation in faculty research project. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities/research-opportunities-program. Not eligible for CR/NCR option.

Credit course for supervised participation in faculty research project. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities/research-opportunities-program. Not eligible for CR/NCR option.

Programming in an interactive statistical environment. Generating random variates and evaluating statistical methods by simulation. Algorithms for linear models, maximum likelihood estimation, and Bayesian inference. Statistical algorithms such as the Kalman filter and the EM algorithm. Graphical display of data.

Probabilistic foundations of supervised and unsupervised learning methods such as naive Bayes, mixture models, and logistic regression. Gradient-based fitting of composite models including neural nets. Exact inference, stochastic variational inference, and Marko chain Monte Carlo. Variational autoencoders and generative adversarial networks.

This course examines current theory of statistical inference, particularly likelihood-based methods and Bayesian methods with an emphasis on resolving present conflicts; log-model expansion and asymptotics are primary tools.

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 partial, multiple and canonical correlations; multivariate analysis of variance; profile analysis and curve fitting for repeated measurements; classification and the linear discriminant function.

Advanced topics in statistics and data analysis with emphasis on applications. Diagnostics and residuals in linear models, introduction to generalized linear models, graphical methods, additional topics such as random effects models, designed experiments, model selection, analysis of censored data, introduced as needed in the context of case studies.

Discrete and continuous time processes with an emphasis on Markov, Gaussian and renewal processes. Martingales and further limit theorems. A variety of applications taken from some of the following areas are discussed in the context of stochastic modeling: Information Theory, Quantum Mechanics, Statistical Analyses of Stochastic Processes, Population Growth Models, Reliability, Queuing Models, Stochastic Calculus, Simulation (Monte Carlo Methods).

Topics of current research interest are covered. Topics vary from year to year. As the necessary academic preparation for this course may vary from year to year, there may be additional prerequisites required, such as specific courses or an application to enrol. Students should contact the department at ug.statistics@utoronto.ca for information on this course, and enrolment in this course, for a given year.

Statistical theory and its applications at an advanced mathematical level. Topics include probability and distribution theory as it specifically pertains to the statistical analysis of data. Linear models and the geometry of data, least squares and the connection to conditional expectation. The basic concept of inference and the likelihood function.

Continuation of STA452H1: statistical theory and its applications at an advanced mathematical level. Topics include classical estimation, theory with methods based on the likelihood function and the likelihood statistics. Testing hypothesis and the evaluation of confidence from both a Bayesian and frequentist point of view.

An overview of methods and problems in the analysis of time series data. Topics include: descriptive methods, filtering and smoothing time series, theory of stationary processes, identification and estimation of time series models, forecasting, seasonal adjustment, spectral estimation, bivariate time series models.

Data acquisition in the environmental, physical, and health sciences are increasingly spatial, and novel in the sense that specialized methods are required for analysis. This course will cover different types of spatial and spatiotemporal data and their analytic methods. Students will learn a variety of advanced techniques for analyzing geostatistical, areal, and point referenced data. Focus will be placed on visualizing spatial data, choosing the correct method for a specific research question, and communicating analytic results clearly and effectively.