Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.

Graduate Courses

Statistics 600

Research Seminar

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) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Also known as:(formerly Statistics 621) MAY BE REPEATED FOR CREDIT NOT INCLUDED IN GPA

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department. MAY BE REPEATED FOR CREDIT

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Also known as:(formerly Statistics 601.14)

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Antirequisite(s):Credit for Statistics 619 and 519 will not be allowed.

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Antirequisite(s):Credit for Statistics 625 and 525 will not be allowed.

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department.

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Antirequisite(s):Credit for Statistics 633 and 533 will not be allowed.

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department.

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department.

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Antirequisite(s):Credit for Statistics 641 and 543 will not be allowed.

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department.

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 and admission to a graduate program in Mathematics and Statistics or consent of the Department.

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):Admission to a graduate program in Mathematics and Statistics or consent of the Department.

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 and admission to a graduate program in Mathematics and Statistics or consent of the Department.