This course is concerned with the concept of financial interest. Topics covered include: interest, discount and present values, as applied to determine prices and values of annuities, mortgages, bonds, equities, loan repayment schedules and consumer finance payments in general, yield rates on investments given the costs on investments.

Reasoning using data is an integral part of our increasingly data-driven world. This course introduces students to statistical thinking and equips them with practical tools for analyzing data. The course covers the basics of data management and visualization, sampling, statistical inference and prediction, using a computational approach and real data.

This course is a basic introduction to statistical reasoning and methodology, with a minimal amount of mathematics and calculation. The course covers descriptive statistics, populations, sampling, confidence intervals, tests of significance, correlation, regression and experimental design. A computer package is used for calculations.

This course covers the basic concepts of statistics and the statistical methods most commonly used in the social sciences. The first half of the course introduces descriptive statistics, contingency tables, normal probability distribution, and sampling distributions. The second half of the course introduces inferential statistical methods. These topics include significance test for a mean (t-test), significance test for a proportion, comparing two groups (e.g., comparing two proportions, comparing two means), associations between categorical variables (e.g., Chi-square test of independence), and simple linear regression.

This course follows STAB22H3, and gives an introduction to regression and analysis of variance techniques as they are used in practice. The emphasis is on the use of software to perform the calculations and the interpretation of output from the software. The course reviews statistical inference, then treats simple and multiple regression and the analysis of some standard experimental designs.

A study of the most important types of financial derivatives, including forwards, futures, swaps and options (European, American, exotic, etc). The course illustrates their properties and applications through examples, and introduces the theory of derivatives pricing with the use of the no-arbitrage principle and binomial tree models.

A mathematical treatment of probability. The topics covered include: the probability model, density and distribution functions, computer generation of random variables, conditional probability, expectation, sampling distributions, weak law of large numbers, central limit theorem, Monte Carlo methods, Markov chains, Poisson processes, simulation, applications. A computer package will be used.

An introduction to probability theory with an emphasis on applications in statistics and the sciences. Topics covered include probability spaces, random variables, discrete and continuous probability distributions, expectation, conditional probability, limit theorems, and computer simulation.

A mathematical treatment of the theory of statistics. The topics covered include: the statistical model, data collection, descriptive statistics, estimation, confidence intervals and P-values, likelihood inference methods, distribution-free methods, bootstrapping, Bayesian methods, relationship among variables, contingency tables, regression, ANOVA, logistic regression, applications. A computer package will be used.

A case-study based course, aimed at developing students’ applied statistical skills beyond the basic techniques. Students will be required to write statistical reports. Statistical software, such as SAS and R, will be taught and used for all statistical analyses.

This course introduces students to statistical software, such as R and SAS, and its use in analyzing data. Emphasis will be placed on communication and explanation of findings. Students will be required to write a statistical report.

The principles of proper collection of data for statistical analysis, and techniques to adjust statistical analyses when these principles cannot be implemented. Topics include: relationships among variables, causal relationships, confounding, random sampling, experimental designs, observational studies, experiments, causal inference, meta-analysis. Statistical analyses using SAS or R.

Students enrolled in the Minor program in Applied Statistics should take STAC53H3 instead.

Statistical models for categorical data. Contingency tables, generalized linear models, logistic regression, multinomial responses, logit models for nominal responses, log-linear models for two-way tables, three-way tables and higher dimensions, models for matched pairs, repeated categorical response data, correlated and clustered responses. Statistical analyses using SAS or R.

This course introduces the principles, objectives and methodologies of data collection. The course focuses on understanding the rationale for the various approaches to collecting data and choosing appropriate statistical techniques for data analysis. Topics covered include elements of sampling problems, simple random sampling, stratified sampling, ratio, regression, and difference estimation, systematic sampling, cluster sampling, elements of designed experiments, completely randomized design, randomized block design, and factorial experiments. The R statistical software package is used to illustrate statistical examples in the course. Emphasis is placed on the effective communication of statistical results.

Principles of statistical reasoning and theories of statistical analysis. Topics include: statistical models, likelihood theory, repeated sampling theories of inference, prior elicitation, Bayesian theories of inference, decision theory, asymptotic theory, model checking, and checking for prior-data conflict. Advantages and disadvantages of the different theories.

This course continues the development of probability theory begun in STAB52H3. Topics covered include finite dimensional distributions and the existence theorem, discrete time Markov chains, discrete time martingales, the multivariate normal distribution, Gaussian processes and Brownian motion.

This course continues the development of probability theory begun in STAC62H3. Probability models covered include branching processes, birth and death processes, renewal processes, Poisson processes, queuing theory, random walks and Brownian motion.

A fundamental statistical technique widely used in various disciples. The topics include simple and multiple linear regression analysis, geometric representation of regression, inference on regression parameters, model assumptions and diagnostics, model selection, remedial measures including weighted least squares, instruction in the use of statistical software.

A mathematical treatment of option pricing. Building on Brownian motion, the course introduces stochastic integrals and Itô calculus, which are used to develop the Black-Scholes framework for option pricing. The theory is extended to pricing general derivatives and is illustrated through applications to risk management.

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.

Linear algebra for statistics. Multivariate distributions, the multivariate normal and some associated distribution theory. Multivariate regression analysis. Canonical correlation analysis. Principal components analysis. Factor analysis. Cluster and discriminant analysis. Multidimensional scaling. Instruction in the use of SAS.

An overview of methods and problems in the analysis of time series data. Topics covered include descriptive methods, filtering and smoothing time series, identification and estimation of times series models, forecasting, seasonal adjustment, spectral estimation and GARCH models for volatility.

Statistical aspects of supervised learning: regression, regularization methods, parametric and nonparametric classification methods, including Gaussian processes for regression and support vector machines for classification, model averaging, model selection, and mixture models for unsupervised learning. Some advanced methods will include Bayesian networks and graphical models.

A survey of statistical techniques used in finance. Topics include mean-variance and multi-factor analysis, simulation methods for option pricing, Value-at-Risk and related risk-management methods, and statistical arbitrage. A computer package will be used to illustrate the techniques using real financial data.

Presents theoretical foundations of machine learning. Risk, empirical risk minimization, PAC learnability and its generalizations, uniform convergence, VC dimension, structural risk minimization, regularization, linear models and their generalizations, ensemble methods, stochastic gradient descent, stability, online learning.

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. Big data sets include data with high-dimensional features and massive sample size. This course introduces the statistical principles and computational tools for analyzing big data: the process of acquiring and processing large datasets to find hidden patterns and gain better understanding and prediction, and of communicating the obtained results for maximal impact. Topics include optimization algorithms, inferential analysis, predictive analysis, and exploratory analysis.

Correlation does not imply causation. Then, how can we make causal claims? To answer this question, this course introduces theoretical foundations and modern statistical and graphical tools for making causal inference. Topics include potential outcomes and counterfactuals, measures of treatment effects, causal graphical models, confounding adjustment, instrumental variables, principal stratification, mediation and interference.

Topics of interest in Statistics, as selected by the instructor. The exact topics can vary from year to year. Enrolment is by permission of the instructor only.

This course is offered by arrangement with a statistics faculty member who must agree to supervise. This course may be taken in any session and must be completed by the last day of classes in the session in which it is taken.

This course is offered by arrangement with a statistics faculty member who must agree to supervise. This course may be taken in any session and must be completed by the last day of classes in the session in which it is taken.