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Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.
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Graduate Courses
Note: Some 500- and 600-level statistics courses may have concurrent lectures. Extra work in these courses (e.g., extra assignments, advanced examination questions, a term project) will be required for credit at the 600 level.
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Statistics
600
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Research Seminar
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A professional skills course, focusing on the development of technical proficiencies that are essential for students to succeed in their future careers as practicing statistician in academia, government, or industry. The emphasis is on delivering professional presentations and using modern statistical research tools. A high level of active student participation is required.
Course Hours:
1.5 units; Q(3S-0)
Also known as:
(formerly Statistics 621)
MAY BE REPEATED FOR CREDIT
NOT INCLUDED IN GPA
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Statistics
601
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Topics in Probability and Statistics
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The content of this course is decided from year to year in accordance with graduate student interest and instructor availability. Topics include but are not restricted to: Advanced Design of Experiments, Weak and Strong Approximation Theory, Asymptotic Statistical Methods, the Bootstrap and its Applications, Generalized Additive Models, Order Statistics and their Applications, Robust Statistics, Statistics for Spatial Data, Statistical Process Control, Time Series Models.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Consent of the Department.
MAY BE REPEATED FOR CREDIT
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Statistics
603
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Applied Statistics for Nursing Research
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Descriptive statistics; probability theory; statistical estimation/inference; power analysis; regression analysis; anova; logistic regression analysis; non-parametric tests; factor analysis; discriminant analysis; Cox's Proportional Hazard Model.
Course Hours:
3 units; H(3-1)
Prerequisite(s):
Statistics 321 or consent of the Department.
Also known as:
(formerly Statistics 601.14)
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Statistics
619
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Bayesian Statistics
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Fundamentals of Bayesian inference, single and multiparameter models, hierarchical models, regression models, generalized linear models, advanced computational methods, Markov chain Monte Carlo.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Statistics 323 or Mathematics 323; Mathematics 267 or 277 or 353 or 381; or consent of the Department.
Antirequisite(s):
Credit for Statistics 619 and 519 will not be allowed.
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Statistics
625
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Multivariate Analysis
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Normal distribution. Statistical inference: confidence regions, hypothesis tests, analysis of variance, simultaneous confidence intervals. Principal components. Factor Analysis. Discrimination and classification. Canonical correlation analysis.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Consent of the Department.
Antirequisite(s):
Credit for Statistics 625 and 525 will not be allowed.
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Statistics
631
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Computational Statistics
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Unconstrained optimization methods, simulation and random number generation, Bayesian inference and Monte Carlo methods, Markov chain Monte Carlo, non-parametric inference, classical inference and other topics. An emphasis will be placed on computational implementation of algorithms.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Consent of the Department.
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Statistics
633
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Survival Models
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Advanced topics in survival models such as the product limit estimator, the cox proportional hazards model, time-dependent covariates, types of censorship.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Statistics 421 or consent of the Department.
Antirequisite(s):
Credit for Statistics 633 and 533 will not be allowed
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Statistics
635
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Generalized Linear Models
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Exponential family of distributions, binary data models, loglinear models, overdispersion, quasi-likelihood methods, generalized additive models, longitudinal data and generalized estimating equations, model adequacy checks.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Statistics 421 or 429 or consent of the Department.
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Statistics
637
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Non-linear Regression
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Topics include but are not restricted to selections from: linear approximations; model specification; various iterative techniques; assessing fit; multiresponse parameter estimation; models defined by systems of differential equations; graphical summaries of inference regions; curvature measures.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Statistics 421 or 429 or consent of the Department.
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Statistics
639
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Conference Course in Actuarial Modelling
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Topics in advanced actuarial theory and practice, such as: insurance risk models; practical analysis of extreme values; advanced property and casualty rate making; actuarial aspects of financial theory.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Consent of the Department.
MAY BE REPEATED FOR CREDIT
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Statistics
641
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Statistical Learning
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Introduction and Linear Regression; Classification; Regularization; Model Assessment and Selection; Support Vector Machines; Unsupervised Learning; Tree-Based Methods; Other Topics (e.g., Neural Networks, Graphical Models, High-Dimensional Data).
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Consent of the Department.
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Statistics
701
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Theory of Probability I
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Probability spaces, integration, expected value, laws of large numbers, weak convergence, characteristic functions, central limit theorems, limit theorems in Rd, conditional expectation, introduction to martingales.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Statistics 321 or Mathematics 321; and Mathematics 353 or 367 or 381.
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Statistics
703
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Theory of Probability II
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Stopping times, renewal theory, martingales, almost sure convergence, Radon-Nikodym derivatives, Doob’s inequality, square integrable martingales, uniform integrability, Markov chains, stationary measure, Birkhoff’s Ergodic Theorem, Brownian motion, stopping times, hitting times, Donsker’s Theorem, Brownian bridge, laws of the iterated logarithm.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Statistics 701.
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Statistics
721
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Statistical Inference
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Statistical models, likelihoods, maximum likelihood estimators, likelihood ratio, Wald and score tests, confidence intervals, bounds and regions, Bayesian estimation and testing, basic large sample theory, estimating equations, jackknife, bootstrap and permutation.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Statistics 323 or Mathematics 323; and Mathematics 353 or 367 or 381.
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Statistics
723
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Theory of Hypothesis Testing
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Likelihood ratio (LR), union-intersection, most powerful, unbiased and invariant tests, Neyman-Pearson Lemma, Karlin-Rubin Theorem, confidence interval (CI), pivotal quantities, shortest length and shortest expected length CI, uniformly most accurate CI, confidence region, simultaneous CI, large-sample tests (Wald’s, score, LR tests), Bayesian hypothesis testing, analysis of variance and linear models.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Statistics 721.
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Courses of Instruction