# Statistics Course Descriptions

**
STAT 800 - Comprehensive Review**

The student will conduct an in-depth literature review of a selected area in Statistics and prepare a report pertaining to the selected topic. The topic will be chosen in consultation with the supervisor and the Department Head. A final examination (written, oral or both) will be conducted by a committee in the Department.

**
STAT 802 - Major Essay in Statistics**

Essay on a selected topic for students in the course-based MSc program in Statistics.

**
STAT 803 - Approved Summer School **

This course is available to full-time Statistics graduate students in good standing. Students will participate in a summer school offered by an approved institute. The school and credit award must be approved by the Graduate Coordinator for Mathematics and Statistics (or designee).
***Prerequisite: Approval of Department Head.***
*Note: Students may only take STAT 803 once in their program.*

**
STAT 818 - Time Series Analysis and Forecasting**

A first graduate course in time series models and analysis. Topics include deterministic and stochastic models, stationary and non-stationary time series models, state space models, spectral analysis, and selected additional topics. This course includes a lab component.
*Note: Students may receive credit for one of STAT 818, STAT 418, or ACSC 418.*

**
STAT 819 - Advanced Applications of Fourier Analysis in Life Sciences**

Advanced applications of Fourier Analysis. Topics include confidence intervals, hypothesis testing, modelling linear relationships, time series and Fourier analysis. Advanced applications of Fourier Analysis in life sciences will be reviewed. The list of applications may vary.

**
STAT 826 - Advanced Survival Analysis**

Life table, survival distributions, types of censoring, estimation and inference for basic survival quantities, proportional hazards regression model, goodness of fit tests.

**
STAT 851 - Probability**

Probability measures; distribution functions; sequences of random variables; characteristic functions; modes of convergence; convergence theorems; weak and strong laws of large numbers; Central Limit Theorem

**
STAT 852 - Statistical Inference**

Detailed theoretical development of statistical interference; statistical models; exponential families, sufficiency; completeness; properties of point estimation; testing hypothesis and confidence regions; asymptotic properties of estimators.

**
STAT 853 - Limit Theorems**

Probability inequalities, weak limit theorems (central limit theorem, weak law of large numbers), strong limit theorems (strong law of large numbers, law of iterated logarithm).

**
STAT 855 - Generalized Linear Models**

Generalized linear models, exponential family, likelihood-based inference, analysis of contingency tables, estimation procedures.

**
STAT 856 - Stochastic Processes**

A first graduate course in stochastic processes. Topics include Markov chains, Poisson process, renewal theory, Brownian motions and selected additional topics. This class is cross-listed with STAT 456 and ACSC 456.

**
STAT 858 - Statistical Modeling of Dependence and Extremes **

A first graduate course in extreme value theory and copula dependence modelling. Topics include copula models, dependence measures, order statistics, maximum domains of attraction, extreme value distribution, peak over threshold method, generalized Pareto distribution and selected additional topics.
***Prerequisite: STAT 851 or permission of the Department Head.***

**
STAT 859 - Design of Experiments**

Completely randomized designs, randomized block designs, factorial and fractional factorial designs, nested designs, fixed and random effects models.

**
STAT 862 - Advanced Topics in Stochastic Processes**

This is an advanced course in stochastic processes. Topics include: Measure theoretic probability theory, stopping theorems, Poisson process, renewal processes, Markov processes, Brownian motion, Gaussian processes, martingales, stochastic integration, and applications.

**
STAT 870 - Bootstrap Methods**

A first course in Bootstrap techniques. Topics include bootstrap and jackknife procedures, confidence intervals, hypotheses testing, standard errors, regression models. Additional topics may vary. jackknife procedures, confidence intervals, hypotheses testing, standard errors, regression models. Additional topics may vary.

**
STAT 872 - Large Sample Methods**

Asymptotic behavior of estimators and test statistics, asymptotic relative efficiency, large sample theory for regression models.

**
STAT 890AD - Analysis of Longitudinal Data**

Exploring longitudinal data. General linear model for longitudinal data. Parametric model for the convariance structure. Generalized linear model for longitudinal data. Likelihood-based methods for categorical data. Missing values for longitudinal data.

**
STAT 890AF - Directed Readings in Stochastic Processes**

Directed readings in Stochastic Processes as selected by the instructor.

**
STAT 890AG - Statistical Analysis with Missing Data**

Missing data is a major issue in statistical analysis. This course introduces the four common approaches for inference in models with missing values, including maximum likelihood, multiple imputation, fully Bayesian, and weighted estimating equations. Computational tools (e.g. the EM algorithm and the Gibbs' sampler) will be discussed.

**
STAT 890AI - Multivariate Statistical Modelling**

Univariate generalized linear models, models for multicategorical responses, multivariate extensions of generalized linear models, selecting and checking models, semi and nonparametric approaches to regression analysis.

**
STAT 890AJ - Statistical Analysis for Language Assessment**

This course explores statistical methods for language test validity and reliability. The main focus will be on Rasch models.

**
STAT 890AR - Stochastic Differential Equations for Finance**

Modelling of mathematical finances in continuous time, stochastic integrals Itô's formula

**
STAT 890AS - Advanced Applied Multivariate Statistics in Educational Psychology**

The purpose of this course is to teach the application of multivariate analysis to research problems in Educational Psychology. This course will include advanced instruction in applied multivariate analysis, including: simple linear regression, multiple regression, nonlinear regression, time-series analysis, logistic regression, MANOVA, factor analysis, between-groups comparison, profile analysis, structural equation modeling and path analysis. The course is designed to broaden one’s understanding of applied statistics, and designing quantitative studies.

**
STAT 890AT - Regression Models for Time Series Analysis**

Times Series Following Generalized Linear Models: Regression Models for Binary Time Series; Regression Models for Categorical Time Series; Regression for Count Time Series; Other models and Alternative ApproachesSTAT Space Models: Prediction and Interpolation

**
STAT 890AW - Statistics in the Health Science**

Function-Based Inference; Likelihood Tenet; Martingale; Bayes Factor; Empirical Likelihood; Jackknife and Bootstrap.

**
STAT 890AX - Computational Statistics**

A general introduction to computational methods in statistics including optimization, statistical estimation algorithms, bootstrapping/jackknife procedures, Monte Carlo sampling, generating random deviates, computation in the R programming language.

**
STAT 900 - Seminar**

Preparation and presentation of a one-hour lecture to graduate students and faculty.

**
STAT 901 - Research**

Thesis research

**
STAT 902 - Research Tools in Statistics**

This course teaches students about the computing and library resources available in the Mathematics and Statistics department. This course also includes an introduction to using LaTeX for preparing papers, writing research proposals, and giving academic presentations.

**
STAT 903 - Comprehensive Exam 1**

Students must complete a comprehensive exam in Probability Theory. The exam will also include one of the following elective topics: Stochastic Processes, Dependence and Extremes, Limit Theorems, or Measure and Integration. It is evaluated on a pass/fail basis.

**
STAT 904 - Comprehensive Exam 2**

Students must complete a comprehensive exam in Statistical Inference. The exam will also include one of the following elective topics: Generalized Linear models, Survival Analysis, Experimental Design, Time Series Analysis, Linear Models, or Sampling Theory. It is evaluated on a pass/fail basis.

**
STAT 905 - Research Proposal**

Students are required to submit a written research proposal for their PhD thesis research project during its early stages. The candidate will give a seminar before the department to defend their proposal. The topic must be approved by the research supervisor and the candidate's PhD committee. It is evaluated on a pass/fail basis. This course is required of all PhD students is Statistics, and will usually be completed following the completion of STAT 903 and 904.