## STA Statistics Courses
Undergraduate seminar that focuses on specific ideas, questions, phenomena or controversies, taught by a regular Faculty member deeply engaged in the discipline. Open only to newly admitted first year students. It may serve as a breadth requirement course; see page 40.
Introduction to the theory of probability, with emphasis on the construction of discrete probability models for applications. After this course, students are expected to understand the concept of randomness and aspects of its mathematical representation. Topics include random variables, Venn diagrams, discrete probability distributions, expectation and variance, independence, conditional probability, the central limit theorem, applications to the analysis of algorithms and simulating systems such as queues.
An introductory course in statistical concepts and methods, emphasizing exploratory data analysis for univariate and bivariate data, sampling and experimental designs, basic probability models, estimation and tests of hypothesis in one-sample and comparative two-sample studies. A statistical computing package is used but no prior computing experience is assumed.
Continuation of STA220H1, emphasizing major methods of data analysis such as analysis of variance for one factor and multiple factor designs, regression models, categorical and non-parametric methods.
Continuation of STA220H1, jointly taught by Statistics and Biology faculty, emphasizing methods and case studies relevant to biologists including experimental design and analysis of variance, regression models, categorical and non-parametric methods.
Introduction to the theory of probability, with emphasis on applications in computer science. The topics covered include random variables, discrete and continuous probability distributions, expectation and variance, independence, conditional probability, normal, exponential, binomial, and Poisson distributions, the central limit theorem, sampling distributions, estimation and testing, applications to the analysis of algorithms, and simulating systems such as queues.
A survey of statistical methodology with emphasis on data analysis and applications. The topics covered include descriptive statistics , data collection and the design of experiments, univariate and multivariate design, tests of significance and confidence intervals, power, multiple regressions and the analysis of variance, and count data. Students learn to use a statistical computer package as part of the course.
A survey of statistical methodology with emphasis on data analysis and applications. The topics covered include descriptive statistics, basic probability, simulation, data collection and the design of experiments, tests of significance and confidence intervals, power, multiple regression and the analysis of variance, and count data. Students learn to use a statistical computer package as part of the course.
This courses deals with the mathematical aspects of some of the topics discussed in STA250H1. Topics include discrete and continuous probability distributions, conditional probability, expectation, sampling distributions, estimation and testing, the linear model.
This course covers probability including its role in statistical modelling. Topics include probability distributions, expectation, continuous and discrete random variables and vectors, distribution functions. Basic limiting results and the normal distribution presented with a view to their applications in statistics.
A sequel to STA257H1 giving an introduction to current statistical theory and methods. Topics include: estimation, testing, and confidence intervals; unbiasedness, sufficiency, likelihood; simple linear and generalized linear models.
Credit course for supervised participation in faculty research project. See page 40 for details.
Analysis of the multiple regression model by least squares; statistical properties of least squares analysis, estimate 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, multicollinearity, variable search method.
Designing samples for valid inferences about populations at reasonable cost: stratification, cluster/multi-stage sampling, unequal probability selection, ratio estimation, control of non-sampling errors (e.g. non-response, sensitive questions, interviewer bias).
Design and analysis of experiments: randomization; analysis of variance; block designs; orthogonal polynomials; factorial designs; response surface methodology; designs for quality control.
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.
Introduction to statistical theory and its application. Basic inference concepts. Likelihood function, Likelihood statistic. Simple large sample theory. Least squares and generalizations, survey of estimation methods. Testing hypotheses, p-values and confidence intervals. Bayesian-fequentist interface. Analysis of Variance from a vector-geometric viewpoint.
An instructor-supervised group project in an off-campus setting. See page 40 for details.
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.
The course discusses foundational aspects of various theories of statistics. Specific topics covered include: likelihood based inference, decision theory, fiducial and structural inference, Bayesian inference.
The course discusses many advanced statistical methods used in the life and social sciences. Emphasis is on learning how to become a critical interpreter of these methodologies while keeping mathematical requirements low. Topics covered include multiple regression, logistic regression, discriminant and cluster analysis, principal components and factor analysis.
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.
An introductory survey of current multivariate analysis, multivariate normal distributions, distribution of multiple and partial correlations, Wishart distributions, distribution of Hotelling’s T2, testing and estimation of regression parameters, classification and discrimination.
Advanced topics in statistics and data analysis with emphasis on applications. Diagnostics and residuals in linear models, introductions to generalized linear models, graphical methods, additional topics such as random effects models, split plot designs, smoothing and density estimation, 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 change from year to year, and students should consult the department for information on material presented in a given year.
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.
Independent study under the direction of a faculty member. Persons wishing to take this course must have the permission of the Undergraduate Secretary and of the prospective supervisor.
Independent study under the direction of a faculty member. Persons wishing to take this course must have the permission of the Undergraduate Secretary and of the prospective supervisor. |

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