Analysis of variance for one-and two-way layouts, logistic regression, loglinear models, longitudinal data, introduction to time series.
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 trends in the environmental, physical and health sciences are increasingly spatial in character and novel in the sense that modern sophisticated methods are required for analysis. This course will cover different types of random spatial processes and how to incorporate them into mixed effects models for Normal and non-Normal data. Students will be trained in a variety of advanced techniques for analyzing complex spatial data and, upon completion, will be able to undertake a variety of analyses on spatially dependent data, understand which methods are appropriate for various research questions, and interpret and convey results in the light of the original questions posed.
An overview of theory and methods in the analysis of survival data. Topics include survival distributions and their applications, parametric and non-parametric methods, proportional hazards regression, and extensions to competing risks and multistate modelling.
Statistical analysis of genetic data is an important emerging research area with direct impact on population health. This course provides an introduction to the concepts and fundamentals of statistical genetics, including current research directions. The course includes lectures and hands-on experience with R programming and state-of-the-art statistical genetics software packages.
Through case studies and collaboration with researchers in other disciplines, students develop skills in the collaborative practice of Statistics. Focus is on pragmatic solutions to practical issues including study design, dealing with common complications in data analysis, and ethical practice, with particular emphasis on written communication. An application must be completed during the priority enrolment period the summer before the course is offered. This online application is available in the Special Enrollment Course section of https://utoronto.sharepoint.com/sites/ArtSci-STA/Undergrad/SitePages/Home.aspx. Priority will be given to students who are completing all requirements of the Specialist in Statistical Science: Methods and Practice or the Applied Statistics Specialist that academic year. Space permitting, students in the Statistics Specialist, the Specialist in Statistical Science: Theory and Methods, the Data Science Specialist, or the Statistics Major will be considered for enrolment in the order in which they applied.
This course is intended for students completing the Statistical Science: Theory and Methods Specialist program. Novel influential ideas and current research topics in statistics will be explored through readings and discussion. Content will generally vary from semester to semester. Student presentations and written reports will be required.
Independent study under the direction of a Department of Statistical Sciences faculty member. There are a limited number of spaces in this course, and capacity varies from year to year based on the availability of faculty supervisors. Enrolment is subject to Department of Statistical Sciences and faculty supervisor approval. Students interested in this course should contact the department at ug.statistics@utoronto.ca for information on how to apply for enrolment in this course in a given year. Not eligible for CR/NCR option.
Independent study under the direction of a Department of Statistical Sciences faculty member. There are a limited number of spaces in this course, and capacity varies from year to year based on the availability of faculty supervisors. Enrolment is subject to Department of Statistical Sciences and faculty supervisor approval. Students interested in this course should contact the department at ug.statistics@utoronto.ca for information on how to apply for enrolment in this course in a given year. Not eligible for CR/NCR option.
Independent study under the direction of a Department of Statistical Sciences faculty member. There are a limited number of spaces in this course, and capacity varies from year to year based on the availability of faculty supervisors. Enrolment is subject to Department of Statistical Sciences and faculty supervisor approval. Students interested in this course should contact the department at ug.statistics@utoronto.ca for information on how to apply for enrolment in this course in a given year. Not eligible for CR/NCR option.